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 remains4°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 1681.7Tenths,
subtract the Height14.89corresp. to .0168,
————
and there remains1666.8|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.