Front matter (continued 3)

19. With the desire of knowing what effect carbonic acid would have on Labarraque’s fluid, and whether it possessed in a greater or smaller degree the power of ordinary acids to expel the chlorine, portions of the solution were put into two Woulfe’s bottles, and a current of carbonic acid gas passed through them. The gas was obtained from sulphuric acid and whitening in a soda-water apparatus, and was well washed in water. The stream of gas brought away small portions of chlorine with it, but they were not sensible to the smell, and could only be detected by putting litmus paper into the current. An immense quantity of gas, equal to nearly 1300 times the volume of the fluid, was sent through; but yet very little chlorine was removed, and the bleaching powers of the fluid were but little diminished, though it no longer appeared alkaline to turmeric paper. Air was then passed through the solution in large quantity; it also removed chlorine, but apparently not quite so much as carbonic acid.

20. One other experiment was made upon the degree in which the carbonate of soda in Labarraque’s liquor resisted decomposition by the chlorine, even at high temperature. Two equal portions of the fluid were taken, and one of them boiled rapidly for fifteen minutes; both were then acted upon by sulphuric acid, blowing, and heat, as described (11), and the two were then tested by nitrate of silver, to ascertain the quantity of chlorine remaining: it was nearly three times as much in the boiled as in the unboiled portion; and by comparing this with the results before obtained (11), it will be seen that, after boiling for a quarter of an hour, not more than a twentieth part of the chlorine had acted upon the alkali, to form chloride and chlorate.

21. It would seem as if I were unacquainted with Dr. Granville’s paper upon this subject, published in the last volume of this Journal, p. 371, were I to close my remarks without taking [p092] any notice of it. Unfortunately, Dr. Granville has mistaken M. Labarraque’s direction, and by passing chlorine, to “complete saturation,” through the carbonate, instead of using the quantities directed, has failed in obtaining Labarraque’s really curious and very important liquid; to which, in consequence, not one of his observations or experiments applies, although the latter are quite correct in themselves.

Royal Institution, Sept. 3, 1827.

HIEROGLYPHICAL FRAGMENTS; with some Remarks on ENGLISH GRAMMAR. In a Letter to the Baron William Von HUMBOLDT. By a Correspondent. ◊

My dear Sir,

I AM happy to tell you that our prospects of new documents from Egypt are very rapidly increasing: Mr. BURTON has had the good fortune to discover at length, in a mosque, the triple inscription for which he has been some years in search; and he has been negotiating with the Pacha for its removal. From its magnitude and state of preservation, there is every reason to believe that it will rival the pillar of Rosetta in its importance, and I sincerely hope that it will tend to check the wildness of conjecture, which has been rioting without bounds in the regions of Egyptian literature. Mr. Tattam is printing a Coptic grammar, and I am preparing an Appendix, which is to contain the rudiments of an Enchorial Lexicon: I ardently wish that Mr. Burton’s inscriptions may come to my assistance before I complete it. I have received nothing from France or from Germany for these four years past: even what is published seems by some fatality to have been withheld from me; and the booksellers send no answers to my commissions. I trust your brother will not forget his kind promise to think of me at Berlin.

I have to thank him and you for your obliging present of your Letter to Abel Remusat on the Genius of the Chinese Language, which has greatly interested me: the best return that I can make will be to give you some remarks which have occurred to me on the language of hieroglyphics in general, [p093] and on the character of the English language, which seems to approach, in its simplicity, as you have yourself observed, to the natural structure of the oldest languages, immediately related to the hieroglyphical form of representation. I fear, however, that I must apologize to you for the want of method with which I shall be obliged at present to throw my fragments together: but it may be allowable to make some difference between a letter and a finished essay.

Hieroglyphics, in their primitive form, are scarcely to be considered in any case as simply a mode of expressing an oral language: they may be a direct and independent representation of our thoughts, that is, of recollections, or sentiments, or intentions, collateral to the representation of the same thoughts by the language of sounds. We find, in many of the Egyptian monuments, a double expression of the same sense: first, a simple picture, for instance, of a votary presenting a vase to a sitting deity; each characterized by some peculiarity of form, and each distinguished also by a name written over him; and this may be called a pure hieroglyphical representation, though it scarcely amounts to a language, any more than the look of love is a language of a lover. But we universally find that the tablet is accompanied by a greater variety of characters which certainly do constitute a language, although we know little or nothing of the sounds of that language; but its import is, that “such a king offers a vase to the deity;” and on the other side, that “the deity grants to the king health and strength, and beauty and riches, and dominion and power.” It is common to see, in these inscriptions, a number of characters introduced, which are evidently identical with some of those in the tablets: and however some of them may occasionally have been employed phonetically, there can be no question of the nature of the changes which their employment must have gone through before they assumed the character of sounds: but this is altogether a separate consideration, and foreign to the present purpose.

Now it is obvious that objects, delineated with the intention of representing the originals to the eye by their form, must necessarily be nouns substantive; and that the picture, containing no verb whatever, can scarcely be said to constitute [p094] either a positive or a negative assertion. At the same time, it must be allowed that a picture of King George the Fourth’s coronation, with the date 19 July 1821, could scarcely be considered otherwise than as asserting a historical truth; and if any emblem of Truth were attached to it, or if it were deposited among the records of other historical facts, it would be equivalent to the expression, “George IV. crowned in July 1821,” which scarcely wants the verb was to convert it into a positive assertion of a fact.

Strictly speaking, however, there seems to be no direct mode of supplying the want of the verb is or was in pure hieroglyphical writing; and if any such sign was employed in the Egyptian or the old Chinese hieroglyphics, its introduction must have been arbitrary or conventional; like the employment of a postulate in mathematics. Every other part of a language appears capable of being reduced, with more or less circumlocution, to the form of a noun substantive; and the English language appears to approach to the Chinese in the facility with which all the forms of grammar may be shaken off.

There is, however, often occasion, in such cases, for a certain degree of metaphor approaching to poetical latitude; and hence it may happen that the least literary nations are sometimes the most poetical. It is, in fact, impossible to exclude metaphor altogether from the most prosaic language; and it is frequently difficult to say where metaphor ends and strict logical prose begins; but by degrees the metaphor drops, and the simple figurative sense is retained. Thus we may say liquid ruby with the same exact meaning as crimson wine; and yet ruby would never be called an adjective, though employed merely to express the colour: in coral lips, however, the coral, first used metaphorically, is converted by habit into an adjective, and the expression is considered as synonymous with labri corallini.

The general custom in English is to place the figurative substantive, used as an adjective by comparison, or by abstraction, before the name which retains its proper sense: thus a chestnut horse is a chestnut like or chestnut coloured horse; a horse chestnut is a coarse kind of chestnut: and in this manner we are enabled to use almost every English noun substantive as an adjective, by an ellipsis of the word like, which, [p095] if inserted entire or abridged, would make a real adjective of the word, as warlike, friendly. But this omission of the termination, like other figures of speech, is easily forgotten in the ordinary forms of language; and the Germans, as well as the English, make use of almost all their substantives in the place of adjectives, though they are more in the habit of continuing them into single long words. When, however, the substantives are so used, they generally become by abstraction real adjectives: for we seldom think of a chestnut, in speaking of the colour of a horse; but the idea of a light brown coat, with an ugly pale-red mane and tail, and a fidgety temper, is very likely to occur to us: and in a horse chestnut the idea of a horse is out of the question; we only think of a coarse fruit which a man cannot eat: so that the true sense, in both these instances, is that of a quality; but coral lips and ivory hands are rather elliptical expressions, composed of two substantives, which might fairly be represented hieroglyphically by the assistance of a branch of coral and an elephant’s tusk. But to describe an abstract quality by any hieroglyphic character, representative of form only, would be generally impossible: colours might be imitated, if we supposed coloured figures to be employed; but other simple ideas, such as those of sound or touch, could never be immediately presented to the eye; and some circuitous invention would always be required for their representation.

Horne Tooke has shewn, with considerable felicity of illustration, that all the parts of speech may be resolved into the noun and the verb; but he has not pointed out so clearly that every verb may be resolved into a noun and the single primitive verb is or was, which, in this sense, may be said to be the only essential verb in any language; as we find, indeed, in the Coptic, that almost every noun becomes a verb, either by the addition of PE, or sometimes even without it. Thus, the morning BLUSHES is synonymous with the morning IS red; he loves justice, with he IS a lover of justice; and I AM an Englishman, with the person now speaking IS an Englishman. But this must be understood of is, was, or will be, in all its tenses; the idea of time, if expressed, being an essential part of the verbal sense.

I confess that some of these reflections have occurred to me in looking over a very singular work, which I had the curiosity [p096] to take up, in order to see what kind of information could be possessed by a person notoriously and professedly ignorant of the origin and relations of the language which he attempts to teach; and, in short, what kind of light could be diffused by an apostle of darkness. Blunders, and some of them ridiculous enough, must, of course, be found in the works of such a person, but most of them are such as every schoolboy might correct; and there really is so much of sagacity in some of Mr. Cobbett’s remarks on the errors of others, that they well deserve the attention of such as are ambitious to write or speak with perfect accuracy.

I shall not attempt to enter into a regular criticism of this Grammar; I shall merely make a few miscellaneous observations, as they have occurred to me in reading it, several of which would be equally applicable to the best of the existing works of a similar nature.

In Letter III we are told that long and short, though adjectives, do not express qualities, but merely dimension or duration; from a singular misconception of the proper sense of the word quality. We find, in Letter IV, the rule given by most grammarians, though not by all, that the article A becomes AN, when it is followed by any word beginning with a vowel; but it is surely more natural to follow the sound than the spelling, and, as we should never think of saying an youthful bride, it seems equally incorrect to say an useful piece of furniture; for the initial sound is precisely the same. In the same manner A unit and A European, seems to sound more agreeable than AN; and the best speakers appear to adopt this custom.

Letter VIII gives us a rule for doubling the last letter of a verb in the participle if an accent is on the last syllable: but it should be observed that the L is doubled, whether accented or not, as in caballing, travelled, levelled, cavilled, controlled. The same letter contains a “List of verbs, which, by some persons, are erroneously deemed irregular,” and which have been so deemed from the time of our German and Saxon ancestors, though Mr. Cobbett thinks it would be more philosophical to conjugate them regularly. Thus we may see at once that freeze may as well give us frozen, as frieren gives the Germans gefroren; that hang may make hung or hanged, according [p097] to its sense, as in German we have hienge from hangen, and hängte from hängen, to execute. For sling and slung, we have authority in schlingen, geschlungen, for spring and sprung in springen and gesprungen; for swollen, swam or swum, and swung, in geschwollen, geschwommen, and geschwungen. And it is quite clear from these examples that “the bad practice of abbreviating, or shortening,” has nothing to do with the matter.

In Letter XIV we have a very distinct examination of a rule in punctuation which has been commonly adopted by good printers, without so distinct a description of its foundation. “Commas are made use of when phrases, that is to say ‘portions’ of words, are ‘throwed’ into a sentence, and which are not absolutely necessary to assist in its grammatical construction.” In a word, two commas are very nearly equivalent to the old fashioned parenthesis. Again, “the apostrophe ought to be called the mark not of elision, but of laziness and vulgarity;” a remark made in truly classical taste, which might have been extended with perfect propriety to the subject of the next paragraph, the Hyphen, the insertion of which is, to make it uncertain whether the words united by it are one word or two. He goes on admirably in the next page. “Notes, like parentheses, are interrupters, and much more troublesome interrupters, because they generally tell a much longer story. The employing of them arises, in almost all cases, from confusion in the mind of the writer. He finds the matter too much for him. He has not the talent to work it all up into one lucid whole; and, therefore, he puts part of it into Notes” . . . . . “Instead of the word and, you often see people put &. For what reason I should like to know. But to this & is sometimes added a c; thus, &c. And is, in Latin, et, and c is the first letter of the Latin word caetera, which means the like, or so on. This abbreviation of a foreign word is a most convenient thing for such writers as have too much indolence or too little sense to say fully and clearly what they ought to say. If you mean to say and the like, or, and so on, why not say it? . . . The abbreviation is very frequently made use of without the writer having any idea of its import.” But it is surely a mischievous maxim, never to “think of mending what you write. Let it go. No [p098] patching; no after painting.” On the other hand he is right in protesting “against the use of what, by some, is called the dash. Who is to know what is intended by the use of these dashes? . . . . It is a cover for ignorance as to the use of points; and it can answer no other purpose.”

In Letter XV, there is a singular conceit with regard to the keeping up a distinction between a and an, where it is insisted that we must not say “a dog, cat, owl, and sparrow,” because owl requires an; “and that it should be, a dog, a cat, an owl, and a sparrow;” which is certainly better, and would be so, even if there were no owl in the question.

Letter XVII. The criticism on Milton’s “than whom none higher sat,” is perfectly correct. Than is never a preposition, and is simply a variation from the older then, both in English and in German. John is better than James means simply John is good first, then James: er is eher or e’er. Who would sound awkwardly, but would be more grammatical.

Letter XIX gives a definition of the ellipsis, which would be a lesson to Apollonius himself: the compasses, it seems, “do not take their sweep all round, but leave out parts of the area or surface.” The objection to Blackstone’s language is very questionable. “The very scheme and model WAS settled,” may, perhaps, be defended, because scheme and model are considered as one thing, the words being intended to illustrate each other, but not to point out different attributes of the administration of justice; and both words may be admitted, as a collective term, to govern a singular rather than a plural verb. It seems also to be an error to make with a conjunction rather than a preposition, and to say “The bag, with the guineas and dollars in it were stolen,” or “zeal, with discretion, do much.” “I expected to have seen,” is justly noticed as a common error for “I expected to see.” The meaning of an active verb is erroneously confounded with that of a transitive verb, in the remarks on the word elope, which means to go off, or to run off, and we should naturally say was gone off, but had run off.

The nature of the subjunctive mood is dismissed in the same Letter without better success than has been obtained by former grammarians. An essay was published about thirty years ago in a periodical work, which brings the subject into a small compass; [p099] suggesting that the subjunctive mood ought always to be considered as a conditional future. The examples given are, “If the Elbe is now open, we shall soon have the mails, and then, if there be any news from the army, I will send it you immediately.” “If Catiline was generous, it was in order to serve his ambition.” The subjunctive past, if I were, becomes present, by being the future of the past; going back to the time when the present was future, and therefore contingent; and this conditional sense involves no difficulty, except when a mistaken adherence to the fancied rules of grammar forces it in where it has no business: thus the rules of some grammarians would lead us to say, if Catiline were ambitious; which is totally contrary to the true sense of the subjunctive. Mr. Cobbett seems to have some such distinctions in view when he says that “if has nothing at all to do with the government of the verb. It is the sense which governs.” By this he means that if does not require a subjunctive unless is relates to a future contingency. He is right in saying “Though her chastity is becoming, it gives her no claim to praise”: but most decidedly wrong in adding “she would be criminal if she was not chaste”; for was is here used as relating to the present circumstances, which are the future of the past, and therefore require the subjunctive were to denote the condition intended. He has, however, done signal justice to the cause of this injured verb, by introducing it for was, in his sixth lesson, where he says it should have been “Your Lordship were apprized of every important circumstance.”

Such errors as this, however, are easily corrected, and many of the acute remarks which have been here copied are well worthy the attention of practical grammarians; at the same time enough has been said, without any disparagement of Cobbett’s talents, to show that a man cannot be well qualified to teach that which he has not had the means of properly learning. For although the English language appears at first sight to be extremely simple and philosophical in its structure, it has, in fact, been derived from a variety of heterogeneous sources; it has undergone a variety of vicissitudes, and has served for the expression of a multiplicity of discussions on the most refined subjects in literature and history and science, for [p100] the feelings of oratory, and the passions of poetry, and it has been worn away by degrees, as the crystal in the stream is worn to a pebble, till it has returned to a simplicity which wears the aspect of the immediate offspring of the Chinese or Egyptian or Mexican Hieroglyphics. But with all this, it has still some spots, some idioms, which invariable custom obliges us to retain; and which can only be distinguished from corruptions and vulgarisms by tracing their history through the different stages of its progress, including, of necessity, the corresponding idioms in the parent languages out of which it has arisen.

Believe me always, my dear Sir,

Your’s very sincerely,

* * * *

Malaria: an Essay on the Production and Propagation of this Poison, and of the Nature and Localities of the Places by which it is produced, with an Enumeration of the Diseases caused by it, and of the Means of diminishing and preventing them, both at Home and in the Naval and Military Service. By J. Mac Culloch, M.D., F.R.S., &c. &c. Longman and Co. 1827. ◊

THOUGH we have given a place in our Journal to two articles on Malaria from Dr. Mac Culloch, we have thought it expedient to take some notice of his book under the form of a review; particularly as some matters have come under our cognizance, which may add some illustrations to this subject where the author appears to have been in a state of deficient information, or to have shunned the question for reasons which appear to us somewhat over refined.

We allude principally here to the localities and the facts, as they are now before us; circumstances and events which seem to us of the greatest importance, as enforcing the value of the details which he has collected, and as holding out warnings to the people respecting the preservation of their healths, in addition to those which the work before us has given in describing the soils or characters of ground in England from which this destructive poison is generated. And before we proceed to the analysis of his book, we shall state what those are, or at least a few of them, while wondering that he should have overlooked them, or regretting that any fancies should have prevented him from stating what would have been of so much utility. [p101]

It is notorious that, in the last autumn, the remittent fevers in various parts of the country amounted to a species of pestilence, such as has scarcely been known in England from this cause, or we might almost indeed say, from any other disease since the days of Sydenham. Wherever ague had ever existed, or even been supposed possible, in those places was this fever found: so that in all the well-known tracts in Lincolnshire, Norfolk, Suffolk, Kent, Essex, Sussex, Hampshire, and so forth, there was scarcely a house without one or more inhabitants under fever, while the event, as might be suspected, was a considerable mortality. In the parish of Marston, in Lincolnshire, for example, it amounted to 25 in 300 inhabitants; in some other places, it reached one in sixteen, one in thirteen, one in nine. And so extensive was its range, that even Hastings did not escape; while it should be almost superfluous to say that every other town on the sea-coast was so much infested by it, that they who resorted to them for bathing, as usual, found themselves most awkwardly situated, and also suffered in considerable numbers.

To come nearer home, and to what must interest us of the metropolis more, the same fevers were extremely abundant in various parts of the outskirts of London, as also in the villages or towns which are connected with it, within a range of from six to ten miles. Not to enumerate all these, this was the case throughout the range of streets or houses which extends from Buckingham Gate to Chelsea; in which long line, it is said, that almost every house had a patient or more under this fever; though, as the author has truly observed, these were mistaken for typhus, or at least thus misnamed. Thus it was also about Vauxhall and Lambeth; and to a great extent among all that scattered mixture of town and country which follows from Whitechapel, from Bishopsgate, and so forth, and very particularly along Ratcliffe Highway, and so on, to an indefinite range along the river, not only on this side but on the opposite one, so as to include Rotherhithe, and then proceeding onward to Deptford, Greenwich, Woolwich, Plumstead, so as to carry us beyond the boundary which we proposed to notice.

And in addition to the towns or villages which we have just named, we may enumerate Lewisham, in which we knew one house in which there were nine patients under this fever, which proved mortal to one. Dulwich, especially subject to this disorder, Fulham, Ealing, and the several other villages along the Thames, as far as Chertsey; and even Richmond, [p102] where, as at Lewisham, there was one house known to us, inasmuch as being intimate friends, where ten individuals at one time were suffering under this disease.

We must not prolong this enumeration, since we might easily occupy a dozen of our pages with similar details, ranging, in fact, all over England; but we must still observe, that whatever was the pestilence last year, it promises to be much greater in the present one. This is easily judged from the manner in which the season has set in; but still more decidedly from the extraordinary prevalence of ague in the spring; since that which is intermittent fever then, will be remittent in the autumn, or rather, as the author has justly remarked, there will scarcely be a definite season of vernal intermittent, but the remittent will commence immediately, increasing in extent and severity as the summer advances, and promising to become, in the autumn, the greatest season of disease that England has known for this century.

As an example of this, it must suffice to enumerate two or three facts, while these are as satisfactory for our purpose as a thousand would be. The most general of these is, that ague is at this moment extremely abundant where it was formerly so little known as not to be noticed, and that where single cases used to occur, there are now hundreds. Thus has it prevailed at Fulham and Ealing, and in the outskirts of London, and even in the town itself; and thus does it so prevail at Greenwich, Deptford, and in the associated vicinity, that a medical friend informs us, that it comprises more than two-thirds of his entire practice, which is very extensive; whereas a few years ago he had rarely a patient in a year. Thus also in the Military Hospital at Woolwich, there were in the spring three hundred patients with this disease; while in former times, we are assured, that an ague was scarcely known once in five or six years.

These are a few of the facts within our knowledge, but not one in a thousand, which evince the necessity of the publication before us; a book which seems to have been singularly well-timed, in as far as its purpose is, by a dissection of the sources of malaria, to diminish the ravages of both these kinds of fevers. And in this view we consider it a work of very considerable utility, inasmuch as it points out all the needful circumstances, as to prevention, in great detail; while these seemed particularly called for in England, from the entire and not less singular neglect which this subject has experienced, not only from the people at large, but from the medical profession. Beyond this, all that we need say of [p103] the character of the work is, that it contains the only regular and complete attempt at the natural history of Malaria that has been executed; since the several foreign writings on this subject are partial, or imperfect, or local in their investigations; and having said thus much, we shall proceed to give a brief analysis of its form and matter. And this analysis may be truly brief, without inconvenience; since the two Essays from the pen of the author, to which we have given a place in our Journal, will supersede the necessity of making that useful and practical abstract which we should otherwise have felt ourselves bound to give.

To pass over an introductory chapter of the usual necessity, the author commences by pointing out the several disorders, in a general way, which are produced by malaria, for the purpose of proving the sources of this poison; and as we are of those who take the facts as already proved, we need not notice it further.

The third chapter details the characters of those soils or situations which are most commonly or generally admitted to produce this poison: and though it contains some facts not very universally known, we shall also pass it over as of less moment than that which follows.

This is the fourth chapter, containing the details of the circumstances producing malaria, which have been either denied or overlooked; and it is one of the most important practical chapters in the book, inasmuch as it is to the popular ignorance of these that we must attribute a large proportion of the cases of fever occurring in common life. These, therefore, we shall mark briefly; and even the briefest notice will be of use in the way of precaution, while we must refer to the book itself for those proofs of the truth of the several views, which we could not take room to give. Generally, however, we may state this leading argument of the author, because it is brief, and, to us, appears satisfactory. It is this: that as the quantity of the poison which any person can inspire is necessarily small, and as this small quantity can be produced by a small marshy spot as well as a large one, it is the same as to the production of disease, whether the marsh is a foot square or a mile, provided the exposure be complete: while also, any piece of ground where vegetables decompose under the action of water, is virtually a marsh, or must produce malaria.

This enumeration, therefore, under that view, comprises, in addition to marshes, whether fresh or salt, all the cases where water is present in such a manner as to act upon vegetables; and the chief are the following. [p104]

It is shown, and by facts, that the rushy swamps of high moorlands, however small the extent, do produce this disease; and we must not here forget to name what, however, belongs to the preceding chapter, woods and coppices, little suspected in England, yet shown to be the cause of fevers in Wales, and also in Sussex; very probably, every where else. It is also shown that meadows and moist pastures, whether in flat lands or on elevations, generate fevers; and very particularly, should they have been affected by inundation or unusual moisture, and if that should be followed by heat. And while it is also specifically shown how, in all cases, it is the produce of the drains or ditches required in meadow lands, it is distinctly proved that, even without these, malaria is produced, or that it is generated by the meadow or moist pasture itself.

It is also shown that this poison is produced by rivers, by all flat rivers at least, or those of which the progress is slow and through meadow lands; while this is pointed out as one of the causes, especially, which is not suspected or not believed in England. And here we can add a fact to our author’s statement, which is decisive: this is the case of the barracks at Morne Bruce, in Dominica, situated on a steep and rocky hill, perfectly dry, and free from all other causes of suspicion, while eternally subject to the most severe fevers. And the cause is, a mountain stream, about 300 yards below this building, in the valley, always covered by a mist in the evenings, and ascertained, by direct experience, to be the very cause of the diseases in question.

Our author also notices canals, mill-ponds, ornamental waters, and all other pools and ponds, even to so small a dimension as those formed in gravel-pits; pointing out those, in particular, as common causes of fever about London, and apparently much inclined to pass a very severe judgment on the canal in St. James’s Park, and also on the pond in St. James’s Square, while apparently restrained by his prudential reasons, which appear to us sufficiently misplaced, or, as we should fairly call them, somewhat absurd. But as we must not affront a writer whose papers we have admitted, we shall say no more on this matter. In noticing drains, he also speaks of moats and modern fortifications; attempting to show that the fevers so common in the sieges of ancient castles were produced by their moats, and noticing the familiar fact of the frequency of fevers in fortified towns. Lakes also are pointed out as situations generating this poison: and it is here especially noticed that if, in those and other cases, malaria is produced by the vegetable growth and decomposition, [p105] so is it the consequence of the exposure of the mud of such receptacles of water; a cause which is again treated of at greater length in the subsequent chapter.

This chapter relates to what the author calls obscure and disputed cases. We shall pass over these, which, as not implying precautionary measures, are of the least interest, and commence by noticing the case of vegetable putrefaction. It is attempted to show, that the vegetable need not be living to produce malaria, but that, even if utterly decomposed, its elements, acting on water, can generate this poison. Among the cases under this head, are flax and hemp ponds, common sewers and drains, dunghills, and tide harbours; and the evidences under each are sufficient to make good the assertion. But the most important of all, in our view at least, is bilge-water: since our author has pretty clearly shown that all the fevers of ships (excepting, of course, a few casual instances of contagion) arise from this cause, and that if ships were kept clean, fever or sickness would be nearly unknown at sea. This we do indeed conceive one of the most important points in the work before us; and if the author has referred to Sir Henry Baynton, as a stranger, we can quote him, as a friend, that warrants for all that is here asserted, and for far more; since his collection of facts on this subject is most important, and we think him almost culpable in not having long ago given them to the public. If the Leviathan was always the healthiest ship in the navy; if she even left the West Indies, after a long anchorage and service, with a crew of 500 men, and not one sick, it is a case in the navy which never occurred before, nor since, and which arose entirely from the knowledge of this able and careful officer respecting the subject that we are discussing.

A sixth chapter explains, under the head of revolutions in the production of malaria, a variety of circumstances not easily admitting of abridgment. The chief of these are, the effects produced by drainages, and reversely, those which arise from inundations or other incidental causes affecting the state of the soil. But the most important view which it contains is that which relates to the effect of embankment in rivers, and to the geological changes produced by the distribution of alluvia. As, however, we cannot well state this in a small space, we shall pass to the chapter on the Propagation of Malaria.

This is the largest, and, as it strikes us, the most interesting of the whole; while the author has made it the depository of a variety of remarks and recommendations on this [p106] subject, very particularly as it relates to the army. If he is correct,—and we see no reason to doubt it, from the nature of the statements,—the ignorance of this subject, even among the medical department of the army, has been most extraordinary and most unaccountable; while if Walcheren is proof enough of this, the writer before us has pointed out facts enough to show that it was not a solitary case, while evidently restrained by fear of some sort—we are almost inclined to call it cowardice—from telling all that he might have told. And we do think it wrong to retain or suppress that which is important to the public safety, under a fear that the feelings of individuals may be hurt; since the business of a writer is with justice and utility, and the security or welfare of thousands is of infinitely greater moment than the comforts of a few, and those also culpable.

Under this head, propagation, the author describes how this poison is conveyed by the winds, while the facts add much to the number and variety of the precautionary measures. And here also we find a speculation of no small curiosity, respecting the East wind, attempting to prove that wherever this is insalubrious or pernicious, it arises from its being the vehicle of malaria; while attempting also to prove that this substance can be conveyed from Holland to the coasts of England in that wind. We shall not pretend to give an opinion on this subject; and since the author himself has noticed it in the paper printed in our present number, we shall suffer our readers to form their own judgments respecting it.

One also of the most curious facts mentioned in this chapter, is the singular limitation of malaria; and we must admit that the instance quoted as to the Chatham road is so remarkable as to be almost incredible; though, as we find that all the people agree in it, we cannot pretend to say it is not a fact. Indeed the facts of this nature, so familiar at Rome, are fully as inexplicable; so that all we can conclude is, that we are ignorant of the philosophy of this subject: no very great cause of surprise, unless it were proved that we could explain every thing else which belongs to meteorology.

In the eighth chapter we have an explanation of the effects of climate and seasons in the production of malaria; and while we need not analyse the facts which it contains, we may introduce in lieu of this, the explanations which its statements afford as to that recent increase of the diseases of malaria which we noticed at the commencement of this article. The last few years have been distinguished for an [p107] uncommon prevalence of East winds, and to such a degree indeed, that we can find no meteorological records at all to be compared with the history of these years. And while the history of the intermittent and remittent, in London at least, from the time of Morton and Sydenham downwards, shows that all its periods of such diseases have been periods of East winds, it is not difficult to see how it acts as to both classes of marsh fever. To London, in particular, it is the best conductor, propagating the malaria from all the moist lands to the eastward. To the East coast, if our author’s theory is valid, it brings the malaria from Holland; and, moreover, as it forms our hottest summers, it causes our own climate to approximate more to the southern ones, and thus enables our lands to produce a greater quantity of malaria than in ordinary summers.

To pass from the eighth chapter, the ninth is a partial sketch of the geography of malaria; a chapter for which the author apologises, but which is nevertheless a very interesting collection of facts on a subject where a volume is, doubtless, a desideratum. And it would require a volume; while, in spite of our author’s fears, we can really see no reason why such a statistical account of health should not be drawn up for England, when the utility of it is unquestionable. It is true that people cannot abandon their homes or change their residences, because their lots happen to be cast in an insalubrious country. But it is not less important to know what and where these dangers are; because, though the inhabitants may be compelled to abide, they can still correct much of the evil by the various modes pointed out, or avoid much of the hazard by resorting to the obvious precautions. To be ignorant, is to be exposed to the full evil: to know where it lies, is to know how and where to avoid it in numerous ways; since it will be found that by far the greater number of diseases occurring, were not necessary or unavoidable, but have been the result of ignorance as to the precise fact or spot which did produce the effect in question. And this we conceive to be the great use of the book before us; and that if ever it, or a code of rules founded on it, shall become popular, or form a vade mecum, particularly in the country, the effect will be to reduce most materially the quantity of disease, and very particularly that which is by far the most serious, the summer and autumnal fevers. On this around, we should be glad to see a geography of malaria for England; and we do hope that it will be undertaken by some person of sufficient industry, and of more [p108] courage than our author; while we cannot doubt that whoever attempts it would at least find it a profitable speculation. With these remarks we must pass over this chapter, as we could take no statement from it which would serve any useful purpose; though, as far as it goes, it will form a very useful guide to travellers on the continent of Europe, or to those who, as emigrants, are in search of a residence abroad.

The tenth chapter examines the inquiries which have been instituted into the chemical nature of malaria, leaving the question just where it was. In fact we, as chemists, do not believe that this science is yet in possession of the means required for analyses of this delicate nature; but we see no reason whatever why it should be despaired of, when chemistry has already, within a very few years, effected things which seemed far more impracticable and hopeless.

The eleventh and last chapter contains an enumeration of the diseases produced by malaria, presenting a most formidable list, and absolutely making us shudder in some of the details which relate to the worst parts of France and Italy. The representation here given of the average of life in these districts is particularly striking; while of the truth of all the facts, we can speak from personal knowledge. Our author has also noticed the effect of this poison on animals; showing that it is the cause of the noted epidemics in cattle, and also of the rot in sheep. If he will look into Livy, he will find a confirmation, which he appears to have passed by when quoting that author for epidemic seasons: this being, that in the same years in which epidemic “pestilences” appeared among the people, there was also a great mortality among the cattle.

We do not know what his own profession will say of his attempt, or rather proposal, to prove that the celebrated disease of the nerves called Tic Douleureux is the produce of malaria and a mode of intermittent fever; nor how they will receive his proposal to arrange Sciatica and Rheumatic pains, with many other local diseases, under this head. But this is not our affair: and as he has promised us two other volumes, on all the diseases which are produced by malaria, including these, we must wait with patience; knowing at least that he is a dealer in facts and not in hypotheses, and expecting, that even if he should fail to establish his point, he will try to do it, as he has been used to do in the other sciences which he has attempted, through the road of facts and evidence. [p109]

An Account of a new Genus of Plants called REEVESIA. By John Lindley, Esq., F.L.S., &c. &c. ◊

IN a collection of dried specimens of plants sent to the Horticultural Society from China, by Mr. Reeves, are a few branches, with flowers, of a remarkable genus which is at present undescribed, but which is of so curious a nature, and of such importance with reference to the determination of some natural affinities, that I have thought it deserving immediate record; especially as drawings of the fruit, which have been subsequently obtained from the same indefatigable correspondent of the Society, render its history tolerably complete.

The branches appear to be fragments of an evergreen tree; they are slender, rounded, and smooth. The nascent gemmæ are covered with a dense rufous pubescence. The leaves are alternate, becoming, towards the extremities of the branches, opposite by approximation; their form is ovate-lanceolate acuminate, and in size they vary from three inches to nearly six in length; the surface, even of the youngest, is perfectly smooth on each side; their veins are inconspicuous, the lowest pair of venæ primariæ being divergent at an angle of about 40°, while the others spread outwards at an angle of 55° or 60°; the venæ arcuatæ and externæ are obscurely seen, but form together a number of rhomboidal spaces, equal in diameter to nearly one third of each side of the leaf; the proportion borne by the petiole to the lamina is variable, sometimes equalling one-fourth of the length of the latter, and not unfrequently being less than one-sixth of its length: this proportion not depending upon the station of the leaves; the petiole is smooth, half-round, and thickened at the extremity, where it unites with the lamina. Stipulæ are none. The flowers are greenish-white, in terminal thyrsoid compound racemes; the upper part of the rachis, and of its branches, is slightly protected by stellate pubescence; the pedicles are closely covered with pubescence of the same nature, and have one subulate downy deciduous bracteola at the base, and another towards the apex. The calyx is inferior, campanulate, tapering a little towards the base, densely clothed with stellate pubescence, bursting irregularly at the apex into [p110] four or five ovate teeth, which are somewhat imbricated during æstivation, but which are separated by the growth of the petals long before the expansion of the flower; the veins of the calyx are remarkably reticulated, and when cut, a considerable quantity of mucilaginous viscid fluid is exuded. The petals are whitish-green, hypogynous, with a convolute æstivation; their ungues are spatulate, and as long as the calyx; their laminæ oblong, spreading flat, and then overlapping each other at the base; at the point of separation of the unguis and lamina is a small callus, and on each side a notch upon the margin. The stamens are seated upon a long, filiform, subclavate, smooth torus; the filaments are consolidated into a capitate five-toothed cup, nearly closed at the orifice, and on the outside of this cup are placed the antheræ, three to each tooth; the latter are two-celled, with divaricating cells, which open longitudinally, and are so entangled with each other that the whole surface of the cup appears, when the antheræ have burst, to consist of a single many-celled anthera. The pollen is spherical and smooth. he ovarium is seated within the cup of stamens, and is so entirely concealed that it cannot be discovered till some part of the cup is removed by violence; it is ovate, smooth, and formed of five inseparable cells, each of which has two ovula placed one above the other, and attached to their placenta by their inner margin; the stigma is sessile, with five radiating lobes. From the Chinese drawing, the half-ripe fruit appears to be fleshy, with five deep angles, and five cells, without any remains of calyx, and with a slight appearance of separation between the lobes. The ripe fruit is an obovate, five-angled, five-celled, five-valved, retuse, woody capsule, with a loculicidal dehiscence, and no separable axis. The seeds are attached one to each side of the valves, and are expanded at their lower end into a wing.

From this description it is obvious that, with the single exception of the contents of the seed, we are in possession of all that it is essential to know of the structure of this plant. The next subject of consideration is its affinity.

The stellate pubescence, the thickening of the petiole at the point where it expands into the lamina, the station of the stamens upon a long, filiform torus, the external position of the [p111] antheræ, and the union of the filaments by threes into a cup surrounding the ovarium, are all characters that forcibly call to recollection the genus Sterculia. The calyx, indeed, in that genus is generally divided much more deeply than in the plant now under consideration, and the antheræ are usually seated at the base of the ovarium; but, on the other hand, in Sterculia colorata of Roxburgh, which, if a distinct genus, (ERYTHROPSIS) as I am inclined to believe; is nevertheless next of kin to Sterculia, the calyx is of the same figure and divided in the same degree, and the antheræ are also combined in a capitate cup inclosing the ovarium. If, however, we pursue this comparison further we find that, with the characters now adverted to, the similarity ceases; in Sterculia there are no petals, the calyx has a valvular not imbricate æstivation, the cells of the fruit separate into distinct folliculi, and do not combine into a solid woody capsule, and the seeds are destitute of wings.

The fruit suggests so obviously some affinity with Pterospermum, that it is next necessary to institute a comparison with that genus. Stellate pubescence, a calyx divided into five portions, five hypogynous unguiculate petals, and fifteen fertile stamens united into a cup, seated on a stipitiform torus, and surrounding the ovarium, a five-celled ovarium, a woody five-celled capsule, with a loculicidal dehiscence, no axis, and winged seeds; all these characters are common to Pterospermum and our plant; but on the other hand the points in which they differ are of much importance. The æstivation of Pterospermum is valvate recurved not imbricate; its calyx is five-parted, not four—five-toothed; its anthers have parallel not divaricating cells, and are seated upon long distinct filaments, not sessile, upon the outside of a capituliform cup; and finally the petioles of the leaves are not connected with the lamina by a thickened space. The seeds are also winged at the apex, not at the base, but upon this point it is not my wish to insist.

If the comparison thus instituted with Pterospermum and Sterculia be attentively considered, we cannot fail to remark that the subject of these observations is nearly equally related to both; to Pterospermum in its petals and fruit, to Sterculia in its calyx and stamens. It must, therefore, be stationed between those two genera, thus confirming the propriety of M. [p112] Kunth’s combination of the Sterculiaceæ of Ventenat with the Byttneriaceæ of Mr. Brown; and, in fact, breaking down every barrier between them.

There are many other points that will suggest themselves to the Botanist, in which this plant is highly worthy of consideration, but for the present it will be enough to give the botanical characters with which it may stand recorded. It is named in honour of John Reeves, Esq., now resident at Canton, to whom we are indebted for our knowledge of it, from whose unwearied exertions in the cause of science the botany of China has received material assistance, and to whom our gardens are indebted for many of the fairest ornaments they contain.

REEVESIA.

Ord. Nat. BYTTNERIACEÆ; Sterculiam (Erythropsin) inter et terospermum.

Calyx campanulatus, 5-dentatus, æstivatione imbricatâ, pube stellatâ tomentosus, bracteolatus. Petala 5, hypogyna, unguiculata, æstivatione convoluta, callo inter unguem et laminam. Stamina in toro longo filiformi insidentia. Antheræ 15, sessiles, in cyatho capituliformi, apice tantum pervio, obsoletè 5-dentato connatæ, extrorsæ, biloculares, loculis divaricatis intricatis, longitudinaliter dehiscentibus. Pollen sphæricum glabrum. Ovarium sessile, intrà cyathum antheriferum, ovatum, glabrum, 5-angulare, 5-loculare, loculis dispermis. Ovula margini loculorum unum super alterum affixa, superiore basi concavo in inferiorem incumbente. Stigma 5-lobum, simplicissimum, sessile. Capsula stipitata, lignosa, obovata, 5-angularis, 5-locularis, loculicidò 5-valvis, axi nullo. Semina cuique loculo duo basi alata.——Arbor (Chinæ) foliis alternis exstipulatis, racemis terminalibus compositis, floribus albis.

1. Reevesia thyrsoidea.

Habitat in China (v. s. sp. in Herb. et iconem in Bibliotheca Soc. Hort.)

[p113]

ASTRONOMICAL AND NAUTICAL COLLECTIONS.

i. Elementary View of the UNDULATORY Theory of LIGHT. By Mr. FRESNEL. ◊ [Continued from the last Number.]

I SHALL not undertake to explain here in detail the reasons and the calculations which lead to the general formulas that I have employed to determine the position of the fringes and the intensity of the inflected rays: but I think it right to give at least a distinct idea of the principles on which this theory rests, and particularly of the principle of interference, which explains the mutual action of the rays of light on each other. The name of interference was given by Dr. YOUNG to the law which he discovered, and of which he has made so many ingenious applications.

This singular phenomenon, so difficult to be satisfactorily explained in the system of emanation, is on the contrary so natural a consequence of the theory of undulation, that it might have been predicted from a general consideration of the principles of that theory. Every body must have observed, in throwing stones into a pond, that, when two groups of waves cross each other on its surface, there are points at which the water remains immoveable, when the two systems are nearly of the same magnitude, while there are other places in which the force of the waves is augmented by their concurrence. The reason of this is easily understood. The undulatory motion of the surface of the water consists of vertical motions, which alternately raise and depress the particles of the fluid. Now, in consequence of the intersection of the waves, it happens, that at certain points of their meeting, one of the two waves has an ascending motion belonging to it, while the other tends at the same instant to depress the surface of the liquid: consequently, when the two opposite impulses are equal, it can neither be actuated by one nor the other, but must remain at rest. On the contrary, at the points in which the motions agree in their direction, and conspire with each other, the liquid, urged in the same direction [p114] by each of the forces, is raised or depressed with a velocity equal to the sum of the effects of the two separate impulses, or to the double of either of them taken singly, since they are now supposed to be equal. Between these points of perfect agreement and complete opposition, which exhibit, one the total absence of motion, the other the maximum of oscillation, there are an infinity of intermediate points, at which the alternate motion takes place with more or less of energy, accordingly as they approach more or less to the places of perfect agreement, or of complete opposition of the two systems of motion which are thus combined, or superinduced on each other.

The waves which are propagated in the interior of an elastic fluid, though very different in their nature from those of a liquid like water, produce mechanical effects by their interference, which are exactly of the same kind, since they consist in alternate oscillatory motions of the particles of the fluid. In fact, it is sufficient that these motions should be oscillatory, that is, that the particles should be carried by them alternately in opposite directions, in order that the effects of one series of waves may be destroyed by those of another series of equal intensity; for, provided that the difference of the route of the two groups of waves [derived from the same origin] be such, that for each point of the fluid the motions in one direction, belonging to the first series, correspond to the motions, belonging to the second, in the opposite direction, they must perfectly neutralise each other, if their intensity is equal: and the particles of the fluid must remain in repose. This result will always hold good, whatever may happen to be the direction of the oscillatory motion, with regard to that in which the undulations are propagated; provided that the direction of the oscillatory motion be the same in the two series to be combined. In the waves which are formed on the surface of a liquid, for example, the direction of the oscillation is [principally] vertical, while the waves are propagated horizontally, and consequently in a direction perpendicular to the former; in the undulations of sound, on the contrary, the oscillatory motion is parallel to the direction of the propagation of the sound, [or rather is [p115] identical with it]; and these undulations, as well as the waves of water, are subject to the laws of interference.

The undulations formed in the interior of a fluid have here been mentioned in a general manner: in order to form a distinct idea of this mode of propagation, it must be remarked, that when the fluid has the same density and the same elasticity in every direction, the agitation produced in any point must be propagated on all sides with the same velocity: for this velocity of propagation, which must not be confounded with the absolute velocity of the particles, depends only on the density and elasticity of the fluid. It follows thence that all the points, agitated at the same instant in a similar manner, must be found in a spherical surface, having for its centre the point which is the origin of the agitation: so that these undulations are spherical, while the waves, which are seen on the surface of a liquid, are simply circular.

We give the name of rays to the right lines drawn from the centre of agitation to the different points of this spherical surface; and these rays are the directions in which the motion is propagated. This is the meaning of the term sonorous rays in acustics, and of luminous rays or rays of light in the system which attributes the phenomena of light to the vibrations of a universal fluid, to which the name of ether has been given.

The nature of the different elementary motions, of which each wave is composed, depends on the nature of the different motions which constitute the primitive agitation. The simplest hypothesis that can be entertained concerning the formation of the luminous undulations, is, that the small oscillations of the particles of the bodies, which produce them, are analogous to those of a pendulum removed but little from its point of rest; for we must conceive the particles of bodies, not as immoveably fixed in the positions which they occupy, but as suspended by forces which form an equilibrium in all directions. Now, whatever the nature of such forces may be, as long as the displacement of the particles is but small in proportion to the extent of their sphere of action, the accelerating force which tends to restore them to their natural position, and which thus causes them to oscillate on each side of it, may always, without sensible error, be considered as proportional [p116] to the magnitude of that displacement: so that the law of their motion must be the same as that of the motion of the pendulum, and of all small oscillations in general. This hypothesis, which is suggested by the analogy with other natural phenomena, and which is the simplest that can be formed respecting the vibrations of the luminous particles, may be considered as experimentally confirmed by the observation, that the optical properties of light are all independent of any circumstances which cause the greatest difference in the intensity of the vibrations: so that the law of their motion must be presumed to be the same for the greatest as for the smallest.

It follows from this hypothesis respecting the small oscillations, that the velocity of the vibrating particle at each instant is proportional to the sine of an arc, representing the time elapsed from the beginning of the motion, taking the circumference for the whole time required for the return of the particle to the same point, that is, the time occupied by two oscillations, the one forwards and the other backwards. Such is the law according to which I have calculated the formulas which serve to determine the effect of any number of systems of waves of which the intensities and the relative positions are given. These formulas will be found in the Annals of Chemistry, vol. xi., page 254: [they may be applied with security to the phenomena there considered, though the perfect accuracy of the hypothesis in all possible cases may be questioned, upon the grounds of the microscopical observations on the motions of vibrating chords, published by Dr. Young in the Philosophical Transactions for 1800. TR.] Without entering into the details of the calculations, I think it necessary to show in what manner the nature of the undulation depends on the kind of motion of the vibrating particles.

Let us suppose, in the fluid, a little solid plane which is removed from its primitive position, towards which it is urged by a force proportional to the distance. At the beginning of its motion, the accelerative force produces in it an infinitely small velocity only; but its action continuing, the effects become accumulated, and the velocity of the solid plane goes on continually to increase, until the moment of its arrival at [p117] the position of equilibrium, in which it would remain, but for the velocity which it has acquired; and it is by this velocity only, that it is carried beyond the point of equilibrium. The same force which tends towards this point, and which now begins to act in a contrary direction, continually diminishes the velocity, until it is completely annihilated; and then the force continuing its action produces a velocity in the contrary direction, which brings the plane back to its place of equilibrium. This velocity again is very small at the commencement of the return of the particle, or plane, and increases by the same degrees as it had before diminished, until the instant of the arrival of the particle at the neutral point, which it passes with the velocity previously acquired: but when it has passed this point, the motion is diminished more and more by the effect of the force tending towards it, and its velocity is reduced to nothing when it arrives at the place of the commencement of the motion. It then recommences, at similar periods, the series of motions which have been described, and would continue to oscillate for ever, but for the effect of the resistance of the surrounding fluid, the inertia of which continually diminishes the amplitude of its oscillations, and finally extinguishes them at the end of a longer or shorter time, according to circumstances. [It must not be inferred from this explanation, that the particles of a fluid transmitting an undulation have any tendency to vibrate for ever: on the contrary it has been admitted by the best writers on the theory of sound, that all the motions which constitute it, as considered in a fluid, are completely transitory in their nature, and have no disposition to be repeated after having been once transmitted to a remoter part of the fluid. TR.]

Let us now consider in what manner the fluid is agitated by these oscillations of the solid plane. The stratum immediately in contact with it, being urged by the plane, receives from it at each instant the velocity of its motion, and communicates it to the neighbouring stratum, which it forces forwards in its turn, and from which the motion is communicated successively to the other strata of the fluid; but this transmission of the motion is not instantaneous, and it is only at the end of a certain time that it arrives at a determinate [p118] distance from the centre of agitation. This time is the shorter, as the fluid is less dense, and more elastic; that is, composed of particles which possess a greater repulsive force. This being granted, let us assume, in order to facilitate the explanation, the moment when the moveable plane is returned to the initial situation, after having performed two complete oscillations in opposite directions: at this moment, the nascent velocity, which it had at first, is transmitted to a stratum of the fluid removed from the centre of agitation by a distance which we may represent by d. Immediately afterwards, the velocity of the moveable plane, which has a little augmented, has been communicated to the stratum in contact with it: “hence it has passed successively through all the following strata;” and at the moment when the first agitation arrives at the stratum of which the distance is d, the second has arrived at the stratum immediately before it. Continuing thus to divide, in our imagination, the duration of the two oscillations of the moveable plane into an infinity of small intervals of time, and the fluid comprehended in the length d, into an equal number of infinitely thin strata, it is easy to perceive, by the same reasoning, that the different velocities of the moveable plane, at each of these instants, are now distributed among the corresponding strata; and that thus, for example, the velocity which the plane possessed at the middle of the first oscillations in the direction of the motion, must have arrived, at the instant in question, at the distance 34 d: so that it is the stratum at this distance which possesses at the moment the greatest direct velocity; and in the same manner when the plane arrived at the limit of its first direct oscillation, its velocity was extinguished, and the same absence of motion will be found at the distance 12 d.

It is always supposed, that the oscillations of the plane are so minute in comparison with the length d, that their extent may be neglected in this calculation: and this hypothesis is actually consistent with the fact, since there is every reason to suppose that the excursions of the incandescent particles are very small in comparison with the extent of an undulation, which, though an extremely minute space, is still an appreciable quantity, and may be actually measured. Besides, [p119] even if the amplitude of these oscillations were not in the first instance so wholly inconsiderable, it would be sufficient to consider an undulation at a greater distance from the centre of agitation, in order that their extent might be diminished in any required proportion.

In the second, or retrograde oscillation, the plane, returning through the same space, must communicate to the stratum of fluid in contact with it, and to the rest in succession, a motion in a direction contrary to that of the first oscillation; for when the plane recedes, the stratum in contact with it, urged against the plane by the elasticity or the expansive force of the fluid, necessarily follows it, and fills up the vacuum which its retrograde motion tends to produce. For the same reason, the second stratum is urged against the first, the third against the second, and so forth. It is thus that the retrograde motion is communicated, step by step, to the most distant strata: its propagation is effected according to the same law that governs the direct motion; the only difference is in the direction of the motions, or, in the language of mathematics, in the sign of the velocities which are imparted to the molecules of the fluid. We see then that the different velocities which have existed in the solid plane, during its second oscillation, must exist at the moment which we are considering, in the different strata comprehended in the other half of d, but with contrary signs. Thus the velocity, for example, which the plane had in the middle of the second oscillation, which is its maximum of retrograde velocity, must now be found in the fluid stratum situated at the distance 14 d from the centre of agitation, while the maximum of direct velocity is found, at the same instant, in the stratum which is at the distance 34 d from the centre of agitation.

The extent of the fluid, agitated by the two opposite oscillations of the solid plane, is what we call the breadth of an entire undulation, and we may consequently give the name of semiundulation to each of the parts actuated by the opposite undulations; the whole constituting a complete oscillation, since it comprehends the return of the vibrating plane to the initial situation. It is obvious, that the two semiundulations, which compose the complete undulation, exhibit, in [p120] the fluid strata which they contain, velocities absolutely equal in magnitude, but with contrary signs, that is to say, carrying the particles of the fluid in opposite directions. These velocities are the greatest in the middle of each of the semiundulations, and decrease gradually towards their extremities, where they entirely vanish: so that the points of rest, and of the greatest velocities positive and negative, are separated from each other by intervals of one fourth of an undulation.

The length of an undulation, d, depends on two things: first, on the promptitude with which the motion is propagated in the fluid; and secondly, the duration of the complete oscillation of the vibrating plane; for the longer this duration, and the more rapid the propagation of the motion, the greater will be the distance to which the first agitation has been extended at the instant of the return of the solid plane to its initial situation. If the oscillations are all performed in the same medium, the velocity of propagation remaining the same, the length of the undulations will be simply proportional to the duration of the oscillations of the vibrating particles from which they originate. As long as the vibrating particles continue to be subjected to the same forces, it follows from the principles of mechanics that each of their minute oscillations will occupy the same time, whatever their extent may be; so that the corresponding undulations of the fluid will continue to be of the same length; they will only differ from each other in the greater or less extent of the elementary vibrations of the particles, which will be proportional to the extent of the luminous particles; for it appears from what has already been stated, that each stratum of the fluid repeats exactly all the motions of the vibrating particle. The greater or less amplitude of the oscillations of the strata of the fluid determines the degree of absolute velocity with which they move, and consequently the energy, but not the nature of the sensation which they excite, which must depend, according to every analogy, upon the duration of the oscillations. It is thus that the nature of the sounds, transmitted by the air to our ears, depends entirely on the duration of each of the oscillations executed by the air, or by the sonorous [p121] body which puts it in motion; and that the greater or less amplitude or energy of the oscillations only augments or diminishes the intensity of the sound, without changing its nature, that is, its tone, or pitch.

The intensity of the light must depend then on the intensity of the vibrations of the ether; and its nature, that is to say, the sensation of colour that it produces, will depend on the duration of each oscillation, or on the length of the undulation, the one of these being proportional to the other. [We find, however, nothing in light of the same colour that is at all analogous to the different register, quality, or timbre of a sound; by which, for instance, the sound of a violin differs from that of a flute in unison with it: the subordinate, or harmonic tones of the sound having nothing in light to correspond with them. TR.]

The duration of the elementary oscillation remaining the same, the absolute velocity of the ethereal particles, at the corresponding periods of the oscillatory motions, is, as we have seen, proportional to its extent. It is the square of this velocity, multiplied by the density of the fluid, that represents what is called the living force in mechanics, or otherwise the energy or impetus of the particles, which is to be taken as the measure of the sensation produced, or of the intensity of the light: thus, for example, if in the same medium, the amplitude of the oscillation is doubled, the absolute velocities will also be doubled, and the living force, or the intensity of the light, will be quadrupled.

We must, however, take care not to confound this absolute velocity of the particles of the fluid with the velocity of the propagation of the agitation. The first varies according to the amplitude of the oscillations; the second, which is nothing but the promptitude with which the motion is communicated from one stratum to the other, is independent of the intensity of the vibrations. It is for this reason, that a weak sound is transmitted by the air with the same velocity as a stronger one; and that the least intense light is propagated with the same rapidity as the brightest. When we speak of the velocity of light, we always speak of the velocity of its propagation. Thus, when we say that light passes through 200 thousand [p122] miles in a second, we do not mean, according to the undulatory system, that such is the absolute velocity of the ethereal particles; but that the motion communicated to the ether employs only a second to pass to a stratum at the distance of 200 thousand miles from its origin.

In proportion as the undulation becomes more distant from the centre of agitation, the motion, spreading over a greater distance, must be weakened in every part of the wave. It is shown by calculation, that the amplitude of the oscillatory motion, or the absolute velocity of the particles concerned in it, is inversely proportional to the distance from the centre of agitation. Consequently, the square of this velocity is inversely proportional to the square of the distance, and the intensity of the light must be inversely as the square of the distance from the luminous point. It must be remarked, that, for the same reasons, the sum of the living forces of the whole undulation remains unaltered; for, on one side the length of the undulation d, which may also be called its thickness, is invariable, and its extent of surface augmenting in proportion to the square of the distance from the centre, the quantity, or mass of the fluid agitated, is proportional to the same square: and since the squares of the absolute velocities are diminished in the same proportion as the masses have augmented, it follows that the sum of the products of the masses by the squares of the velocities, that is to say, the sum of the living forces, remains unaltered. It is a general principle of the motion of elastic fluids, that however the motion may be extended or subdivided, the total sum of the living forces remains constant; and this is the principal reason why the living force must be considered as the measure of light, of which the total quantity always remains very nearly the same, at least as long as it continues to pass through perfectly transparent mediums.

It may be remarked, that black substances, and even the most brilliant metallic surfaces, by no means reflect the whole of the light which falls on them; bodies which are imperfectly transparent, and even the most transparent, when of great thickness, absorb also, to use a common expression, a considerable portion of the light that is passing through [p123] them: but it must not be inferred that the principle of living forces is inapplicable to these phenomena; it follows, on the contrary, from the most probable idea that can be formed of the mechanical constitution of bodies, that the sum of the living force must remain always the same, as long as the accelerating forces tending to bring the particles to their natural positions remain unchanged, and that the quantity of living force which disappears in the state of light, instead of being annihilated, is reproduced in the form of heat.

In order to obtain a correct idea of the manner in which the oscillation of a small solid body occasions undulations in an elastic fluid, it has been only necessary to consider a complete oscillation of the solid plane, which produces an entire undulation. If we suppose the oscillations of the plane to be continually repeated, we shall have a series of undulations instead of a single one: and they will follow each other without intermission, provided that the vibrations of the particle first agitated have been regular. Such a series of regular and uninterrupted luminous motions I call a system of undulations.

It is natural to suppose, on account of the prodigious rapidity of the vibrations of light, that the luminous particles may perform a great number of regular oscillations in each of the different mechanical situations in which they are placed during the combustion or the incandescence of the luminous body, although these circumstances may still succeed each other in extremely short periods; for the millionth part of a second is sufficient to exhibit, for example, 545 millions of undulations of yellow light; so that the mechanical disturbances, which derange the regular succession of the vibrations of the luminous particles, or which even change their nature, might be repeated a million times in a second without preventing the regular succession of more than 500 millions of consecutive undulations in each state of the particle. We shall soon have occasion to apply this observation to the determination of the circumstances in which the interference of luminous waves is capable of producing sensible effects.

We have seen that each undulation produced by an oscillatory motion was composed of two semiundulations, which [p124] occasioned in the particles of the fluids velocities exactly equal in their intensity, though opposite in the direction of the motions. Let us at first suppose that two whole undulations, moving in the same line and in the same direction, differ half an undulation in their progress: they will then be superinduced on each other through one half of their length, or of their breadth, as we should say in speaking of the waves of a liquid: but I here use in preference the term length as applied to the interval between the two points which are similarly affected by the motions of two consecutive undulations. In the supposed case of the coincidence of one half of each of the undulations, the interference will only take place with respect to the parts so coinciding: that is, to the latter half of the first undulation, and the preceding half of the second: and if these two semiundulations are of equal intensity, since they tend to give, to the same points of the ether, impulses directly opposite, they will wholly neutralise each other, and the motion will be destroyed in this part of the fluid, while it will subsist without alteration in the two other halves of the undulations. In such a case, therefore, half of the motion only would be destroyed.

If now we suppose that each of these undulations, differing in their progress by half the whole length of each, is preceded and followed by a great number of other similar undulations; then, instead of the interference of two detached undulations, we must consider the interference of two systems of waves, which may be supposed equal in their number and their intensity. Since, by the hypothesis, they differ half an undulation in their progress, the semiundulations of the one, which tend to cause in the particles of ether a motion in one direction, coincide with the semiundulations of the other, which urge them in the opposite direction, and these two forces hold each other in equilibrium, so that the motion is wholly destroyed in the whole extent of these two systems of waves, except the two extreme semiundulations, which escape from the interference. But these semiundulations will always constitute a very small part of the whole series to be considered.

This reasoning is obviously applicable to such systems only [p125] as are composed of undulations of the same length; for if the waves were longer one than the other, however small their difference might be, it would happen at last that their relative position would not be the same throughout the extent of the groups; and while the first destroyed each other almost completely, the following ones would be less in opposition, and would ultimately agree completely with each other: hence there would arise a succession of weak and strong vibrations analogous to the beatings which are produced by the coincidence of two sounds differing but little from each other in their tone; but these alternations of weaker and stronger light, succeeding each other with prodigious rapidity, would produce in the eye a continuous sensation only.

It is very probable that the impulse of a single luminous semiundulation, or even of an entire undulation, would be too weak to agitate the particles of the optic nerve, as we find that a single undulation of sound is incapable of causing motion in a body susceptible of a sympathetic vibration. It is the succession of the impulse, which, by the accumulation of the single effects, at last causes the sonorous body to oscillate in a sensible manner; in the same manner as the regular succession of the single efforts of a ringer is at last capable of raising the heaviest church bell into full swing. Applying this mechanical idea to vision, supported as it is by so many analogies, we may easily conceive that it is impossible for the two remaining semiundulations, which have been mentioned, to produce any sensible effect on the retina; and that the result of such a combination of the two systems must be the production of total darkness.

If again we suppose the second system of undulations to be again retarded half an undulation more, so as to make the difference of the progress an entire undulation, the coincidence in the motions of the two groups will be again restored, and the velocities of oscillation will conspire and be augmented in the points of superposition; the intensity of the light being then at its maximum.

Adding another semiundulation to the difference in the progress of the two systems, so as to make it an interval and [p126] a half, it is obvious that the semiundulations, superinduced on each other, will now possess opposite qualities, as in the case of the half interval first supposed: and that all the undulations must in this manner be neutralised, except the extreme three semiundulations on each side, which will be free from interference. Thus almost the whole of the motion will again be destroyed, and the combination of the two pencils of light must produce darkness, as in the case first considered.

Continuing to increase the supposed difference by the length of a semiundulation at each step, we shall have alternately complete darkness and a maximum of light, accordingly as the difference amounts to an odd or an even number of semiundulations: that is, supposing always that the systems of undulations are of equal intensity: for if the one series were less vivid than the other, they would be incapable of destroying them altogether: the velocities of the one series would be subtracted from those of the other, since they would tend to move the particles of the ether in contrary directions, but the remainders would still constitute light, though feebler than that of the strongest single pencil. Thus the second pencil would still occasion a diminution of the light: but the diminution would be the less sensible as the pencil is supposed to be weaker.

Such are the consequences of the principle of the interference of undulations, which agree perfectly, as we have seen, with the law of the mutual influence of the luminous rays which is deduced from experiment: for the results are expressed precisely in the same words, if we give the name of length of undulation to the difference of routes which had been represented by the symbol d. Admitting, therefore, as there is every reason to believe, that light consists in the undulations of a subtile fluid, the period d, after which the same effects of interference are repeated, must be the length of an undulation.

It appears from the table already given for the seven principal kinds of coloured rays, that this period d, or the length of the undulation, varies greatly, according to the [p127] colour of the light, and that for the extreme red rays, for example, it is [more than] half as great again as for the violet rays situated at the other extremity of the spectrum.

It may easily be imagined that the number of different undulations is not limited to the seven principal ones which are indicated in the table, and that there must be a multitude of intermediate magnitudes, and others beyond the red and the violet rays: for the ponderable particles, of which the oscillations give rise to them, must be subjected to forces that are infinitely varied, in the combustion or the incandescence of the bodies which excite the motions of the ether: and it is on the energy of these forces that the duration of each oscillation depends, and consequently the length of the undulation produced by it. It is found that all the undulations comprehended [in the air] between the lengths .0000167 E.I. and .0000244, are visible; that is, are capable of exciting vibrations in the optic nerve: the rest are only sensible by their heat, or by the chemical effects which they produce.

It has been remarked, that when two systems of waves differ half an undulation in their progress, two of the semiundulations must escape from interference; that six must be exempt when the difference amounts to three semiundulations; and that, in general, the number of undulations exempt from interference is equal to the number of lengths of a semiundulation separating the corresponding points of the two systems. While this number is very small in proportion to that of the waves contained in each system, the motion must be nearly destroyed, as in the case of the exemption of a single undulation. But it may be imagined that, as we increase the difference of the progress of the two pencils, the undulations exempted from interference may become a material portion of each group, and that it may finally become so great as to separate the groups entirely from each other; and in this case the phenomena of interference would no longer be observable. If, for example, the groups of undulations consisted but of a thousand each, a difference of one-twentieth of an inch in their routes would be much more than sufficient to prevent the interference of the rays of all kinds. [p128]

But there is another much more powerful reason which prevents our perceiving the effects of the mutual influence of the systems of waves when the difference of their routes is considerable; which is the impossibility of rendering the light sufficiently homogeneous: for the most simple light that we can obtain consists still of an infinity of heterogeneous rays, which have not exactly the same length of undulation; and however slight the difference may be, when it is repeated a great number of times, it produces of necessity, as we have already seen, an opposition between the modes of interference of the various rays, which then compensates for the weakening of some by the strengthening of others; [while the shades of colour are not sufficiently distinct to allow the eye to remark the difference.] This is without doubt the principal reason why the effects of the mutual interference of the rays of light become insensible when the difference of the routes is very considerable, so as to amount to 50 or 60 times the length of an undulation.

It has already been laid down as one of the conditions necessary for the appearance of the phenomena of interference, that the rays which are combined should have issued at first from a common source: and it is easy to account for the necessity of this condition by the theory which has now been explained.

Every system of waves, which meets another, always exercises on it the same influence when their relative positions are the same, whether it originates from the same source or from different sources; for it is clear that the reasons, by which their mutual influence has been explained, would be equally applicable to either case. But it is not sufficient that this influence should exist, in order that it may become sensible to our eyes: and for this purpose the effect must have a certain degree of permanence. Now this cannot happen when the two systems of waves which interfere are derived from separate sources. For it is obvious that the particles of luminous bodies, of which the vibrations agitate the ether, and produce light, must be liable to very frequent disturbances in their oscillations, in consequence of the rapid changes which are taking place around them, which may [p129] nevertheless be perfectly reconciled, as we have seen, with the regular continuance of a great number of oscillations in each of the series separated by these perturbations. This being admitted, it is impossible to suppose that these perturbations should take place simultaneously and in the same manner in the vibrations of separate and independent particles; so that it will happen, for example, that the motions of the one will be retarded by an entire semioscillation, while those of the other will be continued without interruption, or will be retarded by a complete oscillation, a change which will completely invert the whole effects of the interference of the two systems of undulations which originate from them; since if they had agreed on the first supposition, they would totally disagree on the second. Now these opposite effects, succeeding each other with extreme rapidity, will produce in the eye a continuous sensation only, which will be a mean between the more or less lively sensations that they excite, and will remain constant, whatever may be the difference of the routes described.

But the case is different when the two luminous pencils originate from a common source: for then the two systems of waves, having originated from the same centre of vibration, undergoing these perturbations in the same manner and at the same instant, undergo no changes in their relative positions: so that if they disagreed in the first instance at any given point, they would continue to disagree at all other times; and if their motions cooperated at first, they would continue to agree as long as the centre of vibration continued to be luminous: so that in this case, the effects must remain constant, and must therefore be sensible to the eye. This is therefore a general principle, applicable to all the effects produced by luminous undulations; that in order to become sensible, they must be permanent.

We have hitherto supposed that the two systems of waves were moving exactly in the same direction, and that consequently their elementary motions, to be combined with each other, were precisely limited to one single line: this is the simplest case of interference, and the only one in which the one motion can be completely destroyed by the other: [p130] for in order that this effect may be produced, not only the two forces must be equal and in contrary directions, but they must also act in the same right line, or be directly opposed to each other.

The phenomenon of coloured rings, and that of the colours developed by polarised light in crystallised plates, present a particular case of interference, in which the undulations are exactly parallel. But in the phenomena of diffraction, or in the experiment with the two mirrors, which has been already described, the rays which interfere always form sensible though very small angles with each other. In these cases the impulses to be combined with each other at the same points, as belonging to the two systems of undulations, will also act in directions forming sensible angles with each other: but on account of the smallness of these angles, the result of the two impulses is almost exactly equal to their sum, when the impulses act in the same direction, and to their difference, when they are in contrary directions. Thus, in the points of agreement or disagreement, the intensity of the light will be the same as if the directions agreed more perfectly; at least the nicest eye will not be able to discover any difference in them. But although, with respect to the intensity of the light, this case of interference resembles that which has already been considered, there are other differences which modify the phenomenon very greatly, both with respect to its general form, and to the circumstances necessary for producing it.

We may take, as a convenient example, the case of diverging rays originating from the same luminous point, and reflected by two mirrors slightly inclined to each other, so as to produce two pencils meeting each other in a sensible angle: the two systems of waves will then meet each other with a slight inclination; and it follows from this obliquity, that if a semiundulation of the first system coincides perfectly in one point with a semiundulation of the second, urging the fluid in the same direction, it must separate from it to the right and left of the point of intersection, and must coincide, a little further off, on one side with the preceding semiundulation which is in a contrary direction, [p131] and on the other side with the following semiundulation, and then be separated from this again, and at a distance twice as great as the first, must coincide with the second semiundulation before and behind it, of which the actions will coincide with its own: whence there will arise, on the surface of this undulation, a series of lines, at equal distances from each other, in which the motion is destroyed and doubled alternately by the action of the second series. Thus if we receive this luminous undulation on a white card, we shall observe on it a series of dark and bright stripes, if the light employed is homogeneous; or coloured fringes of different tints, if we employ white light for the experiment.