Chapter LXXVII
Reading edition
PRACTICE OF THE THIRD EXAMPLE,
REFERRING TO THE SECTIONS.[132]
Section 410. BELOW: Barom. Inches 30, .0168:
Attached Therm. 60°.6; Air-ditto, 60°.2:
Above: Barom. - - Inches 29, .5218:
Attached Therm. 56°.6; Air-ditto, 57°.
Subtract the colder —— from the warmer,
and there remains 4° of Heat to be added
to the colder Barometer; to give it an equal Temperature: which is to be done by the 1st Table, thus:
Section, 356.
To find the Expansion with 4° of Heat, on the colder Barometer; (which, as before, is the upper Barometer) standing at Inches 29, .5218 Tenths.
First, with 4° on 29 Inches = .0117:
2d, with 4° on .5218 Tenths above 29 Inches: In order to obtain which, begin
with 4° on 29 = .0117
then with 4° on 30 = .0121
Subtract for the Expansion with ——
4° on 1 Inch above 29, and there remains .0004.
Section 362.
Then for the Expansion with 4° on .1 Tenth of an Inch above 29 Inches; add a Cypher and decimal Point,
Section 363.
viz. .00004 :
Then for the Expansion on .5128, multiply
the two last Terms, and divide ———
the Product by the first Term .1: the Answer is .0002 |0872
Add the Expansion with 4° on 29 Inches, just found, .0117
to the Inches of the colder Barometer, viz. 29.5218
———
Answer; Inches 29.5337 Tenths of
the colder Barometer, are now expanded equally with the warmer: (rejecting the Decimals as in Section 395.) Place the Barometers, thus:
Upper Barometer, 29.5337
Lower Barometer, 30.0168
End of the first Stage.
Section 371.
411. By the 2d Table, and in the 2d Column, find the Height of each Barometer, with the Standard-Heat, in Feet and Tenths, corresponding to the Inches and nearest Tenth above and below the Point required: and
First of the upper, at 29.5337:
The Inches and nearest Tenth is above Feet.
29.5, corresp. to 2119.7 Difference between .5 and .6 above 29 Inches.
and below 29.6, cor. to 2031.5
———
88|.2
Section 373.
412. By the 3d Table, with the Difference 88 Feet, find the Expansion on the remaining Decimals, above 29.5, viz. on .0337, thus:
on 03 = 26 decimated 26.
003 = 26 2.6
0007 = 62 .62
——
Feet 29.22
From the Height corresponding to 29.5
viz. Feet 2119.7 Tenths,
subtract the 29.22, i. e. Height cor. to .0338
and there ———— ————
remains 2090.4|8, the Height cor. to 29.5338
with Expansion of the Standard-Heat.
413. Repeat the 4 last Steps for the lower Barometer, at 30.0168.
1st. The Inches and nearest Tenth is above
30. corresp. to Feet 1681.7 Difference of .1 above 30 Inches.
and below 30.1 cor. 1595.0
———
86|.7
2d. Then with 86 Feet, find the Expansion on the remaining Decimals, above 30,
viz. .0168, thus: on 01 = 9 9.
006 = 52 5.2
0008 = 69 .69
———
Feet 14.89
414. (3d.) From the Height corresponding to
30 Inches, viz. Feet 1681.7 Tenths,
subtract the Height 14.89 corresp. to .0168,
————
and there remains 1666.8|1, the Height corresp.
to 30.0168, with Expansion of the Standard-Heat.
4th. From the upper Height, at 2090.48
Subtract the lower Height, at 1666.81
———
And there remains the Height 423.67 in Feet
and Tenths of the upper Barometer, with the Standard Temperature.
End of the second Stage.
Section 374.
415. Detached Therm. above 57°
Detached ditto, below 60.2
——
Whole Heat 117.2
Half Heat 58.6 (0 adding a Cypher)
Standard Heat 31.24
———
which being deducted, leaves 27°.36, viz. Degrees
of Heat more than the Standard, for each Barometer.
Section 380.
416. By the 4th Table, find the Expansion of Air, with 27°.36, on Feet 423.67 Tenths.
Section 406.
First, with 27°, on 423.67, thus:
viz. on 400 as 4000 = 262.4 decimated 26.24
20 as 2000 = 131.2 1.312
3 as 3000 = 196.8 .1968
.6 as 6000 = 393.6 .03936
.07 as 7000 = 459.2 .004592
—————
Expansion = 27.692752
Section 407.
Second, with .36 on the same, thus:
on 400 as 4000 = 349.9 decimated .3499
20 as 2000 = 174.9 .01749
3 as 3000 = 262.4 .002624
.6 as 6000 = 524.8 .0005248
.07 as 7000 = 612.3 .00006123
—————
Expansion = .37050003
Add the former 27.692752
—————
Height in Feet 28.06325203
417. Which Height for Expansion of Air, with more than the Standard Heat, being added[133] to the Height, for Expansion of the Barometer, with the Standard-Heat, gives the true Height of the upper Barometer, at the given Heat.
For Expansion of Air above Standard Heat,
Height in Feet 28.0
For Expansion of Barometer,
with Standard: Height in Feet 423.6
———
418. True Height of the upper Barometer 451.6
Lower Barometer 1 Foot above the Water 1.0
Height of the Top of the Cross above the Gallery 50.0
———
Height of the Top of the Cross above the Tyber 502.6
Height of the same, measured the same Day geometrically, was Feet 502.9
End of the last Stage.
