CHAPTER LXXIII.

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.

(See Page 295.)

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. |Difference.| | | | | | 1 | 90309.0 | | | | | 18061.8 | | 2 | 72247.2 | | | | | 10565.4 | | 3 | 61681.8 | | | | | 7496.4 | | 4 | 54185.4 | | | | | 5814.6 | | 5 | 48370.8 | | | | | 4750.9 | | 6 | 43619.9 | | | | | 4016.8 | | 7 | 39603.1 | | | | | 3479.5 | | 8 | 36123.6 | | | | | 3069.2 | | 9 | 33054.4 | | | | | 2745.4 | |10.0 | 30309.0 | | | | | 259.6 | | .1 | 30049.4 | | | | | 256.4 | | .2 | 29793.0 | | | | | 254.3 | | .3 | 29538.7 | | | | | 251.8 | | .4 | 29286.9 | | | | | 249.3 | | .5 | 29037.6 | | | | | 247.0 | | .6 | 28790.6 | | | | | 244.7 | | .7 | 28545.9 | | | | | 242.4 | | .8 | 28303.5 | | | | | 240.2 | | .9 | 28063.3 | | | | | 237.9 | |11.0 | 27825.4 | | | | | 235.8 | | .1 | 27589.6 | | | | | 233.7 | | .2 | 27355.9 | | | | | 231.6 | | .3 | 27124.3 | | | | | 229.6 | | .4 | 26894.7 | | | | | 227.6 | | .5 | 26667.1 | | | | | 225.6 | | .6 | 26441.5 | | | | | 223.7 | | .7 | 26217.8 | | | | | 221.7 | | .8 | 25996.1 | | | | | 220.0 | | .9 | 25776.1 | | | | | 218.0 | |12.0 | 25558.1 | | | | | 216.3 | |12.1 | 25341.8 | | | | | 214.4 | | .2 | 25127.4 | | | | | 212.7 | | .3 | 24914.7 | | | | | 211.0 | | .4 | 24703.7 | | | | | 209.3 | | .5 | 24494.4 | | | | | 207.7 | | .6 | 24286.7 | | | | | 206.0 | | .7 | 24080.7 | | | | | 204.3 | | .8 | 23876.4 | | | | | 202.8 | | .9 | 23673.6 | | | | | 201.2 | |13.0 | 23472.4 | | | | | 199.7 | | .1 | 23272.7 | | | | | 198.2 | | .2 | 23074.5 | | | | | 196.6 | | .3 | 22877.9 | | | | | 195.2 | | .4 | 22682.7 | | | | | 193.7 | | .5 | 22489.0 | | | | | 192.4 | | .6 | 22296.6 | | | | | 191.0 | | .7 | 22105.6 | | | | | 189.4 | | .8 | 21916.2 | | | | | 188.1 | | .9 | 21728.1 | | | | | 186.8 | |14.0 | 21541.3 | | | | | 185.5 | | .1 | 21355.8 | | | | | 184.1 | | .2 | 21171.7 | | | | | 182.9 | | .3 | 20988.8 | | | | | 181.6 | | .4 | 20807.2 | | | | | 180.3 | | .5 | 20626.9 | | | | | 179.0 | | .6 | 20447.9 | | | | | 178.0 | | .7 | 20269.9 | | | | | 176.7 | | .8 | 20093.2 | | | | | 175.4 | | .9 | 19917.8 | | | | | 174.3 | |15.0 | 19743.5 | | | | | 173.1 | |15.1 | 19570.4 | | | | | 172.0 | | .2 | 19398.4 | | | | | 170.9 | | .3 | 19227.5 | | | | | 169.8 | | .4 | 19057.7 | | | | | 168.6 | | .5 | 18889.1 | | | | | 167.6 | | .6 | 18721.5 | | | | | 166.5 | | .7 | 18555.0 | | | | | 165.4 | | .8 | 18389.6 | | | | | 164.1 | | .9 | 18225.5 | | | | | 163.7 | |16.0 | 18061.8 | | | | | 162.4 | | .1 | 17899.4 | | | | | 161.3 | | .2 | 17738.1 | | | | | 160.4 | | .3 | 17577.7 | | | | | 159.3 | | .4 | 17418.4 | | | | | 158.4 | | .5 | 17260.0 | | | | | 157.5 | | .6 | 17102.5 | | | | | 156.5 | | .7 | 16946.0 | | | | | 155.6 | | .8 | 16790.4 | | | | | 154.6 | | .9 | 16635.8 | | | | | 153.7 | |17.0 | 16482.1 | | | | | 152.9 | | .1 | 16329.2 | | | | | 151.9 | | .2 | 16177.3 | | | | | 151.1 | | .3 | 16026.2 | | | | | 150.2 | | .4 | 15876.0 | | | | | 149.3 | | .5 | 15726.7 | | | | | 148.5 | | .6 | 15578.2 | | | | | 147.6 | | .7 | 15430.6 | | | | | 146.8 | | .8 | 15283.8 | | | | | 146.0 | | .9 | 15137.8 | | | | | 145.2 | |18.0 | 14992.6 | | | | | 144.3 | |18.1 | 14848.3 | | | | | 143.6 | | .2 | 14704.7 | | | | | 142.8 | | .3 | 14561.9 | | | | | 142.0 | | .4 | 14419.9 | | | | | 141.2 | | .5 | 14278.7 | | | | | 140.5 | | .6 | 14138.2 | | | | | 139.7 | | .7 | 13998.5 | | | | | 139.0 | | .8 | 13859.5 | | | | | 138.2 | | .9 | 13721.3 | | | | | 137.5 | |19.0 | 13583.8 | | | | | 136.8 | | .1 | 13447.0 | | | | | 136.1 | | .2 | 13310.9 | | | | | 135.3 | | .3 | 13175.6 | | | | | 134.5 | | .4 | 13041.1 | | | | | 134.2 | | .5 | 12906.9 | | | | | 133.3 | | .6 | 12773.6 | | | | | 132.6 | | .7 | 12641.0 | | | | | 131.9 | | .8 | 12509.1 | | | | | 131.3 | | .9 | 12377.8 | | | | | 130.6 | |20.0 | 12247.2 | | | | | 130.0 | | .1 | 12117.2 | | | | | 129.3 | | .2 | 11987.9 | | | | | 128.7 | | .3 | 11859.2 | | | | | 128.0 | | .4 | 11731.2 | | | | | 127.4 | | .5 | 11603.8 | | | | | 126.8 | | .6 | 11477.0 | | | | | 126.2 | | .7 | 11350.8 | | | | | 125.6 | | .8 | 11225.2 | | | | | 125.0 | | .9 | 11100.2 | | | | | 124.4 | |21.0 | 10975.8 | | | | | 123.7 | | .1 | 10852.1 | | | | | 123.3 | | .2 | 10728.8 | | | | | 122.6 | | .3 | 10606.2 | | | | | 122.0 | | .4 | 10484.2 | | | | | 121.5 | | .5 | 10362.7 | | | | | 120.9 | | .6 | 10241.8 | | | | | 120.4 | | .7 | 10121.4 | | | | | 119.8 | | .8 | 10001.6 | | | | | 119.2 | | .9 | 9882.4 | | | | | 118.8 | |22.0 | 9763.6 | | | | | 118.1 | |22.1 | 9645.5 | | | | | 117.7 | | .2 | 9527.8 | | | | | 117.1 | | .3 | 9410.7 | | | | | 116.6 | | .4 | 9294.1 | | | | | 116.0 | | .5 | 9178.1 | | | | | 115.6 | | .6 | 9062.5 | | | | | 115.1 | | .7 | 8947.4 | | | | | 114.5 | | .8 | 8832.9 | | | | | 114.0 | | .9 | 8718.9 | | | | | 113.6 | |23.0 | 8605.3 | | | | | 113.0 | | .1 | 8492.3 | | | | | 112.6 | | .2 | 8379.7 | | | | | 112.1 | | .3 | 8267.6 | | | | | 111.6 | | .4 | 8156.0 | | | | | 111.1 | | .5 | 8044.9 | | | | | 110.6 | | .6 | 7934.3 | | | | | 110.2 | | .7 | 7824.1 | | | | | 109.7 | | .8 | 7714.4 | | | | | 109.3 | | .9 | 7605.1 | | | | | 108.8 | |24.0 | 7496.3 | | | | | 108.3 | | .1 | 7388.0 | | | | | 107.9 | | .2 | 7280.1 | | | | | 107.5 | | .3 | 7172.6 | | | | | 107.0 | | .4 | 7065.6 | | | | | 106.6 | | .5 | 6959.0 | | | | | 106.1 | | .6 | 6852.9 | | | | | 105.7 | | .7 | 6747.2 | | | | | 105.3 | | .8 | 6641.9 | | | | | 104.9 | | .9 | 6537.0 | | | | | 104.4 | |25.0 | 6432.6 | | | | | 104.0 | | .1 | 6328.6 | | | | | 103.6 | | .2 | 6225.0 | | | | | 103.2 | | .3 | 6121.8 | | | | | 102.8 | | .4 | 6019.0 | | | | | 102.4 | | .5 | 5916.6 | | | | | 102.0 | | .6 | 5814.6 | | | | | 101.6 | | .7 | 5713.0 | | | | | 101.2 | | .8 | 5611.8 | | | | | 100.8 | | .9 | 5511.0 | | | | | 100.6 | |26.0 | 5410.4 | | | | | 99.8 | | .1 | 5310.6 | | | | | 99.7 | | .2 | 5210.9 | | | | | 99.3 | | .3 | 5111.6 | | | | | 98.8 | | .4 | 5012.8 | | | | | 98.6 | | .5 | 4914.2 | | | | | 98.1 | | .6 | 4816.1 | | | | | 97.8 | | .7 | 4718.3 | | | | | 97.4 | | .8 | 4620.9 | | | | | 97.0 | | .9 | 4523.9 | | | | | 96.7 | |27.0 | 4427.2 | | | | | 96.4 | | .1 | 4330.8 | | | | | 95.9 | | .2 | 4234.9 | | | | | 95.7 | | .3 | 4139.2 | | | | | 95.2 | | .4 | 4044.0 | | | | | 95.0 | | .5 | 3949.0 | | | | | 94.5 | | .6 | 3854.5 | | | | | 94.3 | | .7 | 3760.2 | | | | | 93.9 | | .8 | 3666.3 | | | | | 93.6 | | .9 | 3572.7 | | | | | 93.2 | |28.0 | 3479.5 | | | | | 92.9 | | .1 | 3386.6 | | | | | 92.6 | | .2 | 3294.0 | | | | | 92.2 | | .3 | 3201.8 | | | | | 91.9 | | .4 | 3109.9 | | | | | 91.6 | | .5 | 3018.3 | | | | | 91.3 | | .6 | 2927.0 | | | | | 90.9 | | .7 | 2836.1 | | | | | 90.7 | | .8 | 2745.4 | | | | | 90.3 | | .9 | 2655.1 | | | | | 90.0 | |29.0 | 2565.1 | | | | | 89.7 | | .1 | 2475.4 | | | | | 89.4 | | .2 | 2386.0 | | | | | 89.1 | | .3 | 2296.9 | | | | | 88.7 | | .4 | 2208.2 | | | | | 88.5 | | .5 | 2119.7 | | | | | 88.2 | | .6 | 2031.5 | | | | | 87.9 | | .7 | 1943.6 | | | | | 87.6 | | .8 | 1856.0 | | | | | 87.3 | | .9 | 1768.7 | | | | | 87.0 | |30.0 | 1681.7 | | | | | 86.7 | | .1 | 1595.0 | | | | | 86.4 | | .2 | 1508.6 | | | | | 86.2 | | .3 | 1422.4 | | | | | 85.8 | | .4 | 1236.6 | | | | | 85.6 | | .5 | 1251.0 | | | | | 85.3 | | .6 | 1165.7 | | | | | 85.0 | | .7 | 1080.7 | | | | | 84.7 | | .8 | 996.0 | | | | | 84.5 | | .9 | 911.5 | | | | | 84.2 | |31.0 | 827.3 | | | | | 83.9 | | .1 | 743.4 | | | | | 83.7 | | .2 | 659.7 | | | | | 83.4 | | .3 | 576.3 | | | | | 83.1 | | .4 | 493.2 | | | | | 82.8 | |31.5 | 410.4 | | | | | 82.6 | | .6 | 327.8 | | | | | 82.4 | | .7 | 245.4 | | | | | 82.0 | | .8 | 163.4 | | | | | 81.8 | | .9 | 81.6 | | | | | 81.6 | |32.0 | 00.0 | | +-----+---------+-----------+

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] (See Page 298.)

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._ | | | ⅒ | 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 — — 39½ Degrees.

The detached Air-Thermometer _below_ was — — 45

1st. Add them, for the whole Heat. — — — 2)84½ Degrees.

2d. For _mean Temperature_ of the Air-Thermometers, or a _Moiety_ of the Heat, divide by 2. — 42¼

3d. Deduct the Standard-Temperature of — — — 31¼ from either Moiety, and the Remainder ——— — — — 11 is the 11 Degrees of Heat, more than the Standard[123] for each Barometer.

For 42°¼, and 42°¼, equal to 84°½, 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°½, 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.