USE AND PRACTICE OF THE SECOND TABLE IN THE FIRST EXAMPLE.

The use.

Section 369. TO find the Heights, in Feet and Tenths, in the Atmosphere, corresponding to the Points at which the Quicksilver stands in both Barometers, which have now the same Temperature, viz. that of the warmer Barometer, on a Supposition that they were both exposed to the Standard-Temperature of 31°.24, on Farenheit’s Scale.

The practice.
The 7th Step applied in the first Example.

370. Look at the first Column, in the second Table, for

25.2, and the Answer is 6225.0 in the second Column; and for

29.4, and the Answer is 2208.2. The Answers are the Heights, in Feet and Tenths, in the Atmosphere, at which the Quicksilver stands in both Barometers, with the Temperature of 31°.24: corresponding to their respective Points, for which sole Purpose this Table is calculated.

371. 8th Step. Having placed the Barometers and their corresponding Heights in the Atmosphere, shewn by the second Table, at one View: subtract the lesser from the whole Height, and there will remain, secondly; (see [Section 367]) the greater Height, viz. the Height corresponding to the Barometer in the elevated Station, above the Height corresponding to the Barometer, on the Ground, (both being at the Temperature of 31°.24) thus:

	Feet.
Inches 25.2 correspond to	6225.0
Inches 29.4 correspond to	2208.2; subtract:
	———
and the Remainder is	4016.8

viz. a Number in Feet and Tenths corresponding to the Height of the upper above the lower Barometer, both being in the Temperature of 31°.34.

THE SECOND TABLE.

The 1st Column shews the Quicksilver in the barometric Tube standing at each Inch from 1 to 10, and at each Tenth from 10 to 32 Inches.

The 2d Column shews the Height of the barometric Tube, above the imaginary Level at 32 Inches,—with the Temperature of 31.24;—in Feet and Tenths, answering to Inches and Tenths of the Barometer in the first Column.

The 3d Column shews the Height in Feet and Tenths, answering to a Tenth of an Inch on the Barometer, being the difference between each two adjoining Heights in the 2d Column.

Inch.	Feet.	Differ- ence.	Inch.	Feet.	Diff.	Inch.	Feet.	Diff.
1	90309.0	18061.8	16.8	16790.4	154.6	24.5	6959.0	106.1
2	72247.2	10565.4	.9	16635.8	153.7	.6	6852.9	105.7
3	61681.8	7496.4	17.0	16482.1	152.9	.7	6747.2	105.3
4	54185.4	5814.6	.1	16329.2	151.9	.8	6641.9	104.9
5	48370.8	4750.9	.2	16177.3	151.1	.9	6537.0	104.4
6	43619.9	4016.8	.3	16026.2	150.2	25.0	6432.6	104.0
7	39603.1	3479.5	.4	15876.0	149.3	.1	6328.6	103.6
8	36123.6	3069.2	.5	15726.7	148.5	.2	6225.0	103.2
9	33054.4	2745.4	.6	15578.2	147.6	.3	6121.8	102.8
10.0	30309.0	259.6	.7	15430.6	146.8	.4	6019.0	102.4
.1	30049.4	256.4	.8	15283.8	146.0	.5	5916.6	102.0
.2	29793.0	254.3	.9	15137.8	145.2	.6	5814.6	101.6
.3	29538.7	251.8	18.0	14992.6	144.3	.7	5713.0	101.2
.4	29286.9	249.3	.1	14848.3	143.6	.8	5611.8	100.8
.5	29037.6	247.0	.2	14704.7	142.8	.9	5511.0	100.6
.6	28790.6	244.7	.3	14561.9	142.0	26.0	5410.4	99.8
.7	28545.9	242.4	.4	14419.9	141.2	.1	5310.6	99.7
.8	28303.5	240.2	.5	14278.7	140.5	.2	5210.9	99.3
.9	28063.3	237.9	.6	14138.2	139.7	.3	5111.6	98.8
11.0	27825.4	235.8	.7	13998.5	139.0	.4	5012.8	98.6
.1	27589.6	233.7	.8	13859.5	138.2	.5	4914.2	98.1
.2	27355.9	231.6	.9	13721.3	137.5	.6	4816.1	97.8
.3	27124.3	229.6	19.0	13583.8	136.8	.7	4718.3	97.4
.4	26894.7	227.6	.1	13447.0	136.1	.8	4620.9	97.0
.5	26667.1	225.6	.2	13310.9	135.3	.9	4523.9	96.7
.6	26441.5	223.7	.3	13175.6	134.5	27.0	4427.2	96.4
.7	26217.8	221.7	.4	13041.1	134.2	.1	4330.8	95.9
.8	25996.1	220.0	.5	12906.9	133.3	.2	4234.9	95.7
.9	25776.1	218.0	.6	12773.6	132.6	.3	4139.2	95.2
12.0	25558.1	216.3	.7	12641.0	131.9	.4	4044.0	95.0
.1	25341.8	214.4	.8	12509.1	131.3	.5	3949.0	94.5
.2	25127.4	212.7	.9	12377.8	130.6	.6	3854.5	94.3
.3	24914.7	211.0	20.0	12247.2	130.0	.7	3760.2	93.9
.4	24703.7	209.3	.1	12117.2	129.3	.8	3666.3	93.6
.5	24494.4	207.7	.2	11987.9	128.7	.9	3572.7	93.2
.6	24286.7	206.0	.3	11859.2	128.0	28.0	3479.5	92.9
.7	24080.7	204.3	.4	11731.2	127.4	.1	3386.6	92.6
.8	23876.4	202.8	.5	11603.8	126.8	.2	3294.0	92.2
.9	23673.6	201.2	.6	11477.0	126.2	.3	3201.8	91.9
13.0	23472.4	199.7	.7	11350.8	125.6	.4	3109.9	91.6
.1	23272.7	198.2	.8	11225.2	125.0	.5	3018.3	91.3
.2	23074.5	196.6	.9	11100.2	124.4	.6	2927.0	90.9
.3	22877.9	195.2	21.0	10975.8	123.7	.7	2836.1	90.7
.4	22682.7	193.7	.1	10852.1	123.3	.8	2745.4	90.3
.5	22489.0	192.4	.2	10728.8	122.6	.9	2655.1	90.0
.6	22296.6	191.0	.3	10606.2	122.0	29.0	2565.1	89.7
.7	22105.6	189.4	.4	10484.2	121.5	.1	2475.4	89.4
.8	21916.2	188.1	.5	10362.7	120.9	.2	2386.0	89.1
.9	21728.1	186.8	.6	10241.8	120.4	.3	2296.9	88.7
14.0	21541.3	185.5	.7	10121.4	119.8	.4	2208.2	88.5
.1	21355.8	184.1	.8	10001.6	119.2	.5	2119.7	88.2
.2	21171.7	182.9	.9	9882.4	118.8	.6	2031.5	87.9
.3	20988.8	181.6	22.0	9763.6	118.1	.7	1943.6	87.6
.4	20807.2	180.3	.1	9645.5	117.7	.8	1856.0	87.3
.5	20626.9	179.0	.2	9527.8	117.1	.9	1768.7	87.0
.6	20447.9	178.0	.3	9410.7	116.6	30.0	1681.7	86.7
.7	20269.9	176.7	.4	9294.1	116.0	.1	1595.0	86.4
.8	20093.2	175.4	.5	9178.1	115.6	.2	1508.6	86.2
.9	19917.8	174.3	.6	9062.5	115.1	.3	1422.4	85.8
15.0	19743.5	173.1	.7	8947.4	114.5	.4	1236.6	85.6
.1	19570.4	172.0	.8	8832.9	114.0	.5	1251.0	85.3
.2	19398.4	170.9	.9	8718.9	113.6	.6	1165.7	85.0
.3	19227.5	169.8	23.0	8605.3	113.0	.7	1080.7	84.7
.4	19057.7	168.6	.1	8492.3	112.6	.8	996.0	84.5
.5	18889.1	167.6	.2	8379.7	112.1	.9	911.5	84.2
.6	18721.5	166.5	.3	8267.6	111.6	31.0	827.3	83.9
.7	18555.0	165.4	.4	8156.0	111.1	.1	743.4	83.7
.8	18389.6	164.1	.5	8044.9	110.6	.2	659.7	83.4
.9	18225.5	163.7	.6	7934.3	110.2	.3	576.3	83.1
16.0	18061.8	162.4	.7	7824.1	109.7	.4	493.2	82.8
.1	17899.4	161.3	.8	7714.4	109.3	31.5	410.4	82.6
.2	17738.1	160.4	.9	7605.1	108.8	.6	327.8	82.4
.3	17577.7	159.3	24.0	7496.3	108.3	.7	245.4	82.0
.4	17418.4	158.4	.1	7388.0	107.9	.8	163.4	81.8
.5	17260.0	157.5	.2	7280.1	107.5	.9	81.6	81.6
.6	17102.5	156.5	.3	7172.6	107.0	32.0	00.0
.7	16946.0	155.6	.4	7065.6	106.6

372. Now apply the third Table, or Table for Tenths, if necessary; including two more Steps, viz. the 9th and 10th: which, being useless, in the first Example, are, for the present, omitted.

373. An Explanation of the third Table, or Table for Tenths, is, however, for the Sake of Order, here subjoined.⁠[122]

THE THIRD TABLE, OR TABLE FOR TENTHS:

Serving to compleat the 2d Table, on Expansion of the Barometer, with the Temperature of 31°.24.

1. The upper horizontal Figures shew the Number of Parts into which the Tenth of an Inch has been divided.

2. The Figures in the left vertical Column express the Height in feet, (above the imaginary Level, at 32 Inches of the Barometer,) or Expansion corresponding to a single Tenth of an Inch of Quicksilver.

3. The feet in the Place of Meeting are called tenths: thus, 90 Feet are 9 Tenths of 100 Feet.

Feet.	Parts into which the Tenth of an Inch is divided.
	1⁄10	2⁄10	3⁄10	4⁄10	5⁄10	6⁄10	7⁄10	8⁄10	9⁄10

81	8	16	24	32	40	49	57	65	73
82	8	16	25	33	41	49	57	66	74
83	8	17	25	33	41	50	58	66	75
84	8	17	25	34	42	50	59	67	76
85	8	17	25	34	42	51	59	68	76
86	9	17	26	34	43	52	60	69	77
87	9	17	26	35	43	52	61	70	78
88	9	18	26	35	44	53	62	70	79
89	9	18	27	36	44	53	62	71	80
90	9	18	27	36	45	54	63	72	81
91	9	18	27	36	45	55	64	73	82
92	9	18	28	37	46	55	64	74	83
93	9	19	28	37	46	56	65	74	84
94	9	19	28	38	47	56	66	75	85
95	9	19	28	38	47	57	66	76	85
96	10	19	29	38	48	58	67	77	86
97	10	19	29	39	48	58	68	78	87
98	10	20	29	39	49	59	69	78	88
99	10	20	30	40	49	59	69	79	89
100	10	20	30	40	50	60	70	80	90
101	10	20	30	40	50	61	71	81	91
102	10	20	31	41	51	61	71	82	92
103	10	21	31	41	51	62	72	82	93
104	10	21	31	42	52	62	73	83	94
105	10	21	31	42	52	63	73	84	94
106	11	21	32	42	53	64	74	85	95
107	11	21	32	43	53	64	75	86	96
108	11	22	32	43	54	65	76	86	97
109	11	22	33	44	54	65	76	87	98
110	11	22	33	44	55	66	77	88	99
111	11	22	33	44	55	67	78	89	100
112	11	22	34	45	56	67	78	90	101
113	11	23	34	45	56	68	79	90	102
114	11	23	34	46	57	68	80	91	103
115	11	23	34	46	57	69	80	92	103
116	12	23	35	46	58	70	81	93	104
117	12	23	35	47	58	70	82	94	105
118	12	24	35	47	59	71	83	94	106
119	12	24	36	48	59	71	83	95	107
120	12	24	36	48	60	72	84	96	108
121	12	24	36	48	60	73	85	97	109
122	12	24	37	49	61	73	85	98	110
123	12	25	37	49	61	74	86	98	111
124	12	25	37	50	62	74	87	99	112
125	12	25	37	50	62	75	87	100	112
126	13	25	38	50	63	76	88	101	113
127	13	25	38	51	63	76	89	102	114
128	13	26	38	51	64	77	90	102	113
129	13	26	39	52	64	77	90	103	116
130	13	26	39	52	65	78	91	104	117

END OF THE SECOND STAGE.

374. The Ends proposed in the third and last Stage of the Work, are, first, to add the general Temperatures of the Air, or detached Air-Thermometers, at each Place of Observation above and below, into one Sum.

Secondly, to divide that Sum: each Moiety of which is called the mean Temperature of the Air.

Thirdly, to apply that Moiety to each Barometer, (both of which have been already brought to the Standard-Temperature of 31°. 24;) in order to prove whether the Moiety (or Quantity of Heat assigned to each Barometer by the general Temperature of the Air) exceeded, fell short of, or equalled the Standard-Temperature of the Barometers, by the 2d Table.

And fourthly, from the Moiety or mean Temperature of the Air, to find the true Height of the upper Barometer: which Temperature resolves itself into three Cases.

375. 1st. If the Moiety or mean Temperature of the Air is greater than the Standard Temperature, viz. that to which the Barometers are now brought; find the Expansion of Air corresponding to such Excess of Temperature by the fourth Table, which Height by Expansion, being added to the Height already found in the 2d Table, shews the true Height, viz. of the upper Barometer.

N. B. The 3d and last Stage includes two Steps only, viz, 11th and 12th.

376. 11th Step. The detached Air-Thermometer above was	391⁄2	Degrees.
The detached Air-Thermometer below was	45
1st. Add them, for the whole Heat.	2)841⁄2
2d. For mean Temperature of the Air-Thermometers, or a Moiety of the Heat, divide by 2.	421⁄4
3d. Deduct the Standard-Temperature of	311⁄4
	——
from either Moiety, and the Remainder	11

is the 11 Degrees of Heat, more than the Standard⁠[123] for each Barometer.

For 42°1⁄4, and 42°1⁄4, equal to 84°1⁄2, was the whole Height of the Air at both Places of Observation in the upper and lower Stations; of which whole Height the detached or Air-Thermometer above received 39°1⁄2, and the detached or Air-Thermometer below, received 45°.

377. 12th Step. Find the Height corresponding to the Expansion of Air, with Excess of Heat or Temperature above the Standard-Temperature of the Barometers: and add it (as in the first Example) to the Height of the upper Barometer, corresponding to the Standard-Temperature already found in the second Table, and the Sum is the true Height of the upper Barometer.

This is to be done by referring to the 4th Table, shewing Expansion of Air with Heat; for the Application of which there are separate Instructions: see the Explanation of the 4th Table.⁠[124]

378. The Expansion of Air, in the first Example, is found by the 4th Table to be Feet 107.3 Tenths higher than the 4016.8, viz. the Remainder from the 2d Table ([Section 371]); which Numbers added give 4124.1 Feet: viz. the true Height of the upper Station required.