Note 38 — PART SECOND. NOTES ON THE ILLUMINATION OF LIGHTHOUSES, WITH SHORT NOTICES OF THEIR EARLY HISTORY.

That the form of a flame is necessarily conoidal, and that its height is determined by the relation subsisting between its diameter and the continually varying velocities of the currents of gas and air, may be easily shewn; and the combustion of each annular film of the stream of gas from the wick can take place only at a level determined by, and continually varying with, the ratio of the velocities of the streams of gas and air. I am unwilling to offer this explanation in my own words, when those of M. Peclet, in his excellent work, Traité de l’Eclairage, are at hand,—“Let us conceive,” says he, “a very thin film or layer of inflammable gas placed horizontally, and which rises into the air parallel to itself, with a uniform motion. We shall suppose that it cannot be burnt, except at its circumference, and that the top and bottom of the film are, by some means, preserved from combustion (they are so preserved in ordinary flames, by the films which precede and follow them). If the circumference is at a high enough temperature it will burn; at each instant the film or layer of air, which has assisted the combustion and also the products of that combustion, being very hot, will rise very rapidly, and will make room for other layers or films of air, which will rise in their turn; and as the diameter of the film of gas is continually diminishing, it is obvious that its combustion will offer the appearance of a series of circles continually growing smaller, and terminating at length in a point. If we trace in thought the series of circles which the combustion has successively developed, we shall form a cone whose length will depend on the ratio of the velocities of the films of gas and of air which escape after combustion. If, for example, the velocity of the current of air were very great, compared to the velocity of the cylinder of gas, the entire combustion would take place, while the film of gas passes over a very small space; and the cone formed by the succession of luminous circles would, consequently, be very short. If, on the contrary, there were but a very small difference between these velocities, the luminous circles would only appear at considerable intervals from each other; for the air which had served for combustion, being unable to feed it longer, the surface of the cylinder could not become luminous until the difference of velocity had freed it from the air which had served for the preceding combustion. If, then, we imagine a set of similar films succeeding each other, each of them would give rise to the same series of coloured rings; and as there would be a film in each section of the cone in a state of combustion at the same instant of time, the cone would, of course, appear luminous throughout its height.”—Peclet, Traité de l’Eclairage, p. 51.