Chapter LXXXII: 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:

[Sidenote: 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.

[Sidenote: Section 362.]

Then for the Expansion _with_ 4° _on_ .1 Tenth of an Inch above 29 Inches; add a Cypher and decimal Point, viz. .00004:

[Sidenote: Section 363.]

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._

[Sidenote: 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
and below 29.6, cor. to 2031.5 } between .5 and .6
—————— } above 29 Inches.
88|.2 }

[Sidenote: 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
and _below_ 30.1 cor. 1595.0 } .1 above 30
—————— } Inches.
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._

[Sidenote: 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.

[Sidenote: Section 380.]

416. By the 4th Table, find the Expansion of Air, with 27°.36, on Feet 423.67 Tenths.

[Sidenote: 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

[Sidenote: 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._