Chapter LXXIII
Reading edition
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.
