CHAPTERLXXIIII.USE AND PRACTICE OF THE FOURTH TABLE, IN THE FIRST EXAMPLE.Theuse.Section 379.TO shew in Feet, and Tenths, what is the Expansion of Air on each thousand Feet, from 1000 to 9000 Feet,witheach Degree of Temperature from 1 to 100 Degrees, on Farenheit’s Scale.Thepractice.The 12th Step applied in the first Example.380. For the Expansion of Air with 11 Degrees of Heat on 4016.8 Feet, look in the fourth Table,with11 in the left Hand vertical Column of Temperature, and (first)on4000 Feet, along the upper Line: the Place of Meeting gives the Expansion of the Air,with11 Degreeson4000 Feet: viz. 106.92.[126]Next; lookwith11 Degrees, and (as there is a Cypher only in the Place of Hundreds)on10,(viz. of the 16 Feet) call the 10, a 1000; the Place of Meeting, or Answer is 26.73:Thirdly;with11,on6, (viz. of the 16,) calling it 6000; the Answer is 160.38:Fourthly;with11,on8, (viz. the .8,) and the Answer is 213.84.381. Having added the respective Expansions together, thus;with11°,on4016.8Feet. Tenths.with11°on}4000=106.92106.9210=26.73.26736=160.38.16038.8=213.84.021384—————Expansion107.369064;THE FOURTH TABLE,shewing the expansion with HEAT, from 1 to 100 degrees, on each THOUSAND FEET in the atmosphere, from 1000 to 9000 feet.degrees of the THERMOMETER, from 1 to 50, on farenheit’s scale.10002000300040005000600070008000900012.434.867.299.7212.1514.5817.0119.4421.8724.869.7214.5819.4424.3029.1634.0238.8843.7437.2914.5821.8729.1636.4543.7451.0358.3265.6149.7219.4429.1638.8848.6058.3268.0477.7687.48512.1524.3036.4548.6060.7572.9085.0597.20109.35614.5829.1643.7458.3272.9087.49102.06116.64131.22717.0134.0251.0368.0485.05102.06119.07136.08153.09819.4438.8858.3277.7697.20116.64136.08155.52174.96921.8743.7465.6187.48109.35131.22153.09174.96196.831024.3048.6072.9097.20121.50145.80170.10194.40218.701126.7353.4680.19106.92133.65160.38187.11213.84240.571229.1658.3287.48116.64145.80174.96204.12233.28262.441331.5963.1894.77126.36157.95189.54221.13252.72284.311434.0268.04102.06136.08170.10204.12238.14272.16306.181536.4572.90109.35145.80182.25218.70255.15291.60328.051638.8877.76116.64155.52194.40233.28272.16311.04349.921741.3182.62123.93165.24206.55247.86289.17330.48371.791843.7487.48131.22174.96218.70262.44306.18349.92393.661946.1792.34138.51184.68230.85277.02323.19369.36415.532048.6097.20145.80194.40243.00291.60340.20388.80437.402151.03102.06153.09204.12255.15306.18357.21408.24459.272253.46106.92160.38213.84267.30320.76374.22427.68481.142355.89111.78167.67223.56279.45335.34391.23447.12503.012458.32116.64174.96233.28291.60349.92408.24466.56524.882560.75121.50182.25243.00303.75364.50425.25486.00546.752663.18126.36189.54252.72315.90379.08442.26505.44568.622765.61131.22196.83262.44328.05393.66459.27524.88590.492868.04136.08204.12272.16340.20408.24476.28544.32612.362970.47140.94211.41281.88352.35422.82493.29563.76634.233072.90145.80218.70291.60364.50437.40510.30583.20656.103175.33150.66225.99301.32376.65451.98527.31602.64677.973277.76155.52233.28311.04388.80466.56544.32622.08699.843380.19160.38240.57320.76400.95481.14561.33641.52721.713482.62165.24247.86330.48413.10495.72578.34660.96743.583585.05170.10255.15340.20425.25510.30595.35680.40765.453687.48174.96262.44349.92437.40524.88612.36699.84787.323789.91179.82269.73359.64449.55539.46629.37719.28809.193892.34184.68277.02369.36461.70554.04646.38738.72831.063994.77189.54284.31379.08473.85568.62663.39758.16852.934097.20194.40291.60388.80486.00583.20680.40777.60874.804199.63199.26298.89398.52498.15597.78697.41797.04896.6742102.06204.12306.18408.24510.30612.36714.42816.48918.5443104.49208.98313.47417.96522.45626.94731.43835.92940.4144106.92213.84320.76427.68534.60641.52748.44855.36962.2845109.35218.70328.05437.40546.75656.10765.45874.80984.1546111.78223.56335.34447.12558.90670.68782.46894.241006.0247114.21228.42342.63456.84571.05685.26799.47913.681027.8948116.64233.28349.92466.56583.20699.84816.48933.121049.7649119.07238.14357.21476.28595.35714.42833.49952.561071.6350121.50243.00364.50486.00607.50729.00850.5972.001093.551123.93247.86371.79495.72619.65743.58867.51991.441115.3752126.36252.72379.08505.44631.80758.16884.521010.881137.2453128.79257.58386.37515.16643.95772.74901.531030.321159.1154131.22262.44393.66524.88656.10787.32918.541049.761180.9855133.65267.30400.95534.60668.25801.90935.551069.201202.8556136.08272.16408.24544.32680.40816.48952.561088.641224.7257138.51277.02415.53554.04692.55831.06969.571108.081246.5958140.94281.88422.82563.76704.70845.64986.581127.521268.4659143.37286.74430.11573.48716.85860.221003.591146.961290.3360145.80291.60437.40583.20729.00874.801020.601166.401312.2061148.23296.46444.69592.92741.15889.381037.611185.841334.0762150.66301.32451.98602.64743.30903.961054.621205.281355.9463153.09306.18459.27612.36755.45918.541071.631224.721377.8164155.52311.04466.56622.08767.60933.121088.641244.161399.6865157.95315.90473.85631.80779.75947.701105.651263.601421.5566160.38320.76481.14641.52791.90962.281122.661283.041443.4267162.81325.62488.43651.24814.05976.861139.671302.481465.2968165.24330.48495.72660.96826.20991.441156.681321.921487.1669167.67335.34503.01670.68838.351006.021173.691341.361509.0370170.10340.20510.30680.40850.501020.601190.701360.801530.9071172.53345.06517.59690.12862.651035.181207.711380.241552.7772174.96349.92524.88699.84874.801049.761224.721399.681574.6473177.39354.78532.17709.56886.951064.341241.731419.121596.5174179.82359.64539.46719.28899.101078.921258.741438.561618.3875182.25364.50546.75729.00911.251093.501275.751458.001640.2576184.68369.36554.04738.72923.401108.081292.761477.441662.1277187.11374.22561.33748.44935.551122.661309.771496.881683.9978189.54379.08568.62758.16947.701137.241326.781516.321705.8679191.97383.94575.91767.88959.851151.821343.791535.761727.7380194.40388.80583.20777.60972.001166.401360.801555.201749.6081196.83393.66590.49787.32984.151180.981377.811574.641771.4782199.26398.52597.78797.04996.301195.561394.821594.081793.3483201.69403.38605.07806.761008.451210.141411.831613.521815.2184204.12408.24612.36816.481020.601224.721428.841632.961837.0885206.55413.10619.65826.201032.751239.301445.851652.401858.9586208.98417.96626.94835.921044.901253.881462.861671.841880.8287211.41422.82634.23845.641057.051268.461479.871691.281902.6988213.84427.68641.52855.361069.201283.041496.881710.721924.5689216.27432.54648.81865.081081.351297.621513.891730.161946.4390218.70437.40656.10874.801093.501312.201530.901749.601968.3091221.13442.26663.39884.521105.651326.781547.911769.041990.1792223.56447.12670.68894.241117.801341.361564.921788.482012.0493225.99451.98677.97903.961129.951355.941581.931807.922033.9194228.42456.84685.26913.681142.101370.521598.941827.362055.7895230.85461.70692.55923.401154.251385.101615.951846.802077.6596233.28466.56699.84933.121166.401399.681632.961866.242099.5297235.71471.42707.13942.841178.551414.261649.971885.682121.3998238.14476.28714.42952.561190.701428.841666.981905.122143.2699240.57481.14721.71962.281212.851443.421683.991924.562165.13100243.00486.00729.00972.001215.001458.001701.001944.002187.00382. The decimal Points in the Answer must be changed, thus:1. For the Place ofThousandsin the Question, (viz. 4000,) the Answer must remain, viz. 106.92, as in the Table, which is calculated for the Place ofThousands.2. For the Place ofHundreds, in the Question, (viz. which in the present Case was a Cypher;) if there had been a Figure or Figures in the Place of hundreds; then the decimal Point in the Answer must have been removed overoneFigure or Place to the left.3. For the Place ofTens, in the Question, (viz. 10 Feet,) the decimal Point in the Answer, must be removed overtwoFigures, or Places, to the left.4. For the Place ofUnits, in the Question, (viz. 6) the decimal Point in the Answer, must be removed overthreeFigures, or Places, to the left.5. For the Place of aDecimal, in the Question, (viz. .8) the decimal Point, in the Answer, must be removed overfourFigures, or Places to the left, by adding a Cypher: and for the Place of each further Decimal in the Question;—onePlace more in the Answer, by the further occasional Addition of a Cypher, thus:onFeet 4000,the Ans. 106.92is still 106.921026.73becomes .26736160.38.16038.8213.84.021384—————107.369064383. Which Sum, by rejecting all but the firstDecimal, in the Answer, is Feet 107.3 Tenths equal to the Expansion of Air,with11° of Heat,on4016.8 Feet, the Height of the upper Barometer, with the Temperature of 31°.24, according to the 2d Table.
CHAPTERLXXIIII.
Section 379.TO shew in Feet, and Tenths, what is the Expansion of Air on each thousand Feet, from 1000 to 9000 Feet,witheach Degree of Temperature from 1 to 100 Degrees, on Farenheit’s Scale.
380. For the Expansion of Air with 11 Degrees of Heat on 4016.8 Feet, look in the fourth Table,with11 in the left Hand vertical Column of Temperature, and (first)on4000 Feet, along the upper Line: the Place of Meeting gives the Expansion of the Air,with11 Degreeson4000 Feet: viz. 106.92.[126]
Next; lookwith11 Degrees, and (as there is a Cypher only in the Place of Hundreds)on10,(viz. of the 16 Feet) call the 10, a 1000; the Place of Meeting, or Answer is 26.73:
Thirdly;with11,on6, (viz. of the 16,) calling it 6000; the Answer is 160.38:
Fourthly;with11,on8, (viz. the .8,) and the Answer is 213.84.
381. Having added the respective Expansions together, thus;
4016.8
Feet. Tenths.
with11°on
4000
=
106.92
106.92
10
=
26.73
.2673
6
=
160.38
.16038
.8
=
213.84
.021384
—————
Expansion
107.369064;
shewing the expansion with HEAT, from 1 to 100 degrees, on each THOUSAND FEET in the atmosphere, from 1000 to 9000 feet.
1
2.43
4.86
7.29
9.72
12.15
14.58
17.01
19.44
21.87
2
4.86
9.72
14.58
19.44
24.30
29.16
34.02
38.88
43.74
3
7.29
14.58
21.87
29.16
36.45
43.74
51.03
58.32
65.61
4
9.72
19.44
29.16
38.88
48.60
58.32
68.04
77.76
87.48
5
12.15
24.30
36.45
48.60
60.75
72.90
85.05
97.20
109.35
6
14.58
29.16
43.74
58.32
72.90
87.49
102.06
116.64
131.22
7
17.01
34.02
51.03
68.04
85.05
102.06
119.07
136.08
153.09
8
19.44
38.88
58.32
77.76
97.20
116.64
136.08
155.52
174.96
9
21.87
43.74
65.61
87.48
109.35
131.22
153.09
174.96
196.83
10
24.30
48.60
72.90
97.20
121.50
145.80
170.10
194.40
218.70
11
26.73
53.46
80.19
106.92
133.65
160.38
187.11
213.84
240.57
12
29.16
58.32
87.48
116.64
145.80
174.96
204.12
233.28
262.44
13
31.59
63.18
94.77
126.36
157.95
189.54
221.13
252.72
284.31
14
34.02
68.04
102.06
136.08
170.10
204.12
238.14
272.16
306.18
15
36.45
72.90
109.35
145.80
182.25
218.70
255.15
291.60
328.05
16
38.88
77.76
116.64
155.52
194.40
233.28
272.16
311.04
349.92
17
41.31
82.62
123.93
165.24
206.55
247.86
289.17
330.48
371.79
18
43.74
87.48
131.22
174.96
218.70
262.44
306.18
349.92
393.66
19
46.17
92.34
138.51
184.68
230.85
277.02
323.19
369.36
415.53
20
48.60
97.20
145.80
194.40
243.00
291.60
340.20
388.80
437.40
21
51.03
102.06
153.09
204.12
255.15
306.18
357.21
408.24
459.27
22
53.46
106.92
160.38
213.84
267.30
320.76
374.22
427.68
481.14
23
55.89
111.78
167.67
223.56
279.45
335.34
391.23
447.12
503.01
24
58.32
116.64
174.96
233.28
291.60
349.92
408.24
466.56
524.88
25
60.75
121.50
182.25
243.00
303.75
364.50
425.25
486.00
546.75
26
63.18
126.36
189.54
252.72
315.90
379.08
442.26
505.44
568.62
27
65.61
131.22
196.83
262.44
328.05
393.66
459.27
524.88
590.49
28
68.04
136.08
204.12
272.16
340.20
408.24
476.28
544.32
612.36
29
70.47
140.94
211.41
281.88
352.35
422.82
493.29
563.76
634.23
30
72.90
145.80
218.70
291.60
364.50
437.40
510.30
583.20
656.10
31
75.33
150.66
225.99
301.32
376.65
451.98
527.31
602.64
677.97
32
77.76
155.52
233.28
311.04
388.80
466.56
544.32
622.08
699.84
33
80.19
160.38
240.57
320.76
400.95
481.14
561.33
641.52
721.71
34
82.62
165.24
247.86
330.48
413.10
495.72
578.34
660.96
743.58
35
85.05
170.10
255.15
340.20
425.25
510.30
595.35
680.40
765.45
36
87.48
174.96
262.44
349.92
437.40
524.88
612.36
699.84
787.32
37
89.91
179.82
269.73
359.64
449.55
539.46
629.37
719.28
809.19
38
92.34
184.68
277.02
369.36
461.70
554.04
646.38
738.72
831.06
39
94.77
189.54
284.31
379.08
473.85
568.62
663.39
758.16
852.93
40
97.20
194.40
291.60
388.80
486.00
583.20
680.40
777.60
874.80
41
99.63
199.26
298.89
398.52
498.15
597.78
697.41
797.04
896.67
42
102.06
204.12
306.18
408.24
510.30
612.36
714.42
816.48
918.54
43
104.49
208.98
313.47
417.96
522.45
626.94
731.43
835.92
940.41
44
106.92
213.84
320.76
427.68
534.60
641.52
748.44
855.36
962.28
45
109.35
218.70
328.05
437.40
546.75
656.10
765.45
874.80
984.15
46
111.78
223.56
335.34
447.12
558.90
670.68
782.46
894.24
1006.02
47
114.21
228.42
342.63
456.84
571.05
685.26
799.47
913.68
1027.89
48
116.64
233.28
349.92
466.56
583.20
699.84
816.48
933.12
1049.76
49
119.07
238.14
357.21
476.28
595.35
714.42
833.49
952.56
1071.63
50
121.50
243.00
364.50
486.00
607.50
729.00
850.5
972.00
1093.5
51
123.93
247.86
371.79
495.72
619.65
743.58
867.51
991.44
1115.37
52
126.36
252.72
379.08
505.44
631.80
758.16
884.52
1010.88
1137.24
53
128.79
257.58
386.37
515.16
643.95
772.74
901.53
1030.32
1159.11
54
131.22
262.44
393.66
524.88
656.10
787.32
918.54
1049.76
1180.98
55
133.65
267.30
400.95
534.60
668.25
801.90
935.55
1069.20
1202.85
56
136.08
272.16
408.24
544.32
680.40
816.48
952.56
1088.64
1224.72
57
138.51
277.02
415.53
554.04
692.55
831.06
969.57
1108.08
1246.59
58
140.94
281.88
422.82
563.76
704.70
845.64
986.58
1127.52
1268.46
59
143.37
286.74
430.11
573.48
716.85
860.22
1003.59
1146.96
1290.33
60
145.80
291.60
437.40
583.20
729.00
874.80
1020.60
1166.40
1312.20
61
148.23
296.46
444.69
592.92
741.15
889.38
1037.61
1185.84
1334.07
62
150.66
301.32
451.98
602.64
743.30
903.96
1054.62
1205.28
1355.94
63
153.09
306.18
459.27
612.36
755.45
918.54
1071.63
1224.72
1377.81
64
155.52
311.04
466.56
622.08
767.60
933.12
1088.64
1244.16
1399.68
65
157.95
315.90
473.85
631.80
779.75
947.70
1105.65
1263.60
1421.55
66
160.38
320.76
481.14
641.52
791.90
962.28
1122.66
1283.04
1443.42
67
162.81
325.62
488.43
651.24
814.05
976.86
1139.67
1302.48
1465.29
68
165.24
330.48
495.72
660.96
826.20
991.44
1156.68
1321.92
1487.16
69
167.67
335.34
503.01
670.68
838.35
1006.02
1173.69
1341.36
1509.03
70
170.10
340.20
510.30
680.40
850.50
1020.60
1190.70
1360.80
1530.90
71
172.53
345.06
517.59
690.12
862.65
1035.18
1207.71
1380.24
1552.77
72
174.96
349.92
524.88
699.84
874.80
1049.76
1224.72
1399.68
1574.64
73
177.39
354.78
532.17
709.56
886.95
1064.34
1241.73
1419.12
1596.51
74
179.82
359.64
539.46
719.28
899.10
1078.92
1258.74
1438.56
1618.38
75
182.25
364.50
546.75
729.00
911.25
1093.50
1275.75
1458.00
1640.25
76
184.68
369.36
554.04
738.72
923.40
1108.08
1292.76
1477.44
1662.12
77
187.11
374.22
561.33
748.44
935.55
1122.66
1309.77
1496.88
1683.99
78
189.54
379.08
568.62
758.16
947.70
1137.24
1326.78
1516.32
1705.86
79
191.97
383.94
575.91
767.88
959.85
1151.82
1343.79
1535.76
1727.73
80
194.40
388.80
583.20
777.60
972.00
1166.40
1360.80
1555.20
1749.60
81
196.83
393.66
590.49
787.32
984.15
1180.98
1377.81
1574.64
1771.47
82
199.26
398.52
597.78
797.04
996.30
1195.56
1394.82
1594.08
1793.34
83
201.69
403.38
605.07
806.76
1008.45
1210.14
1411.83
1613.52
1815.21
84
204.12
408.24
612.36
816.48
1020.60
1224.72
1428.84
1632.96
1837.08
85
206.55
413.10
619.65
826.20
1032.75
1239.30
1445.85
1652.40
1858.95
86
208.98
417.96
626.94
835.92
1044.90
1253.88
1462.86
1671.84
1880.82
87
211.41
422.82
634.23
845.64
1057.05
1268.46
1479.87
1691.28
1902.69
88
213.84
427.68
641.52
855.36
1069.20
1283.04
1496.88
1710.72
1924.56
89
216.27
432.54
648.81
865.08
1081.35
1297.62
1513.89
1730.16
1946.43
90
218.70
437.40
656.10
874.80
1093.50
1312.20
1530.90
1749.60
1968.30
91
221.13
442.26
663.39
884.52
1105.65
1326.78
1547.91
1769.04
1990.17
92
223.56
447.12
670.68
894.24
1117.80
1341.36
1564.92
1788.48
2012.04
93
225.99
451.98
677.97
903.96
1129.95
1355.94
1581.93
1807.92
2033.91
94
228.42
456.84
685.26
913.68
1142.10
1370.52
1598.94
1827.36
2055.78
95
230.85
461.70
692.55
923.40
1154.25
1385.10
1615.95
1846.80
2077.65
96
233.28
466.56
699.84
933.12
1166.40
1399.68
1632.96
1866.24
2099.52
97
235.71
471.42
707.13
942.84
1178.55
1414.26
1649.97
1885.68
2121.39
98
238.14
476.28
714.42
952.56
1190.70
1428.84
1666.98
1905.12
2143.26
99
240.57
481.14
721.71
962.28
1212.85
1443.42
1683.99
1924.56
2165.13
100
243.00
486.00
729.00
972.00
1215.00
1458.00
1701.00
1944.00
2187.00
382. The decimal Points in the Answer must be changed, thus:
1. For the Place ofThousandsin the Question, (viz. 4000,) the Answer must remain, viz. 106.92, as in the Table, which is calculated for the Place ofThousands.
2. For the Place ofHundreds, in the Question, (viz. which in the present Case was a Cypher;) if there had been a Figure or Figures in the Place of hundreds; then the decimal Point in the Answer must have been removed overoneFigure or Place to the left.
3. For the Place ofTens, in the Question, (viz. 10 Feet,) the decimal Point in the Answer, must be removed overtwoFigures, or Places, to the left.
4. For the Place ofUnits, in the Question, (viz. 6) the decimal Point in the Answer, must be removed overthreeFigures, or Places, to the left.
5. For the Place of aDecimal, in the Question, (viz. .8) the decimal Point, in the Answer, must be removed overfourFigures, or Places to the left, by adding a Cypher: and for the Place of each further Decimal in the Question;—onePlace more in the Answer, by the further occasional Addition of a Cypher, thus:on
Feet 4000,
the Ans. 106.92
is still 106.92
10
26.73
becomes .2673
6
160.38
.16038
.8
213.84
.021384
—————
107.369064
383. Which Sum, by rejecting all but the firstDecimal, in the Answer, is Feet 107.3 Tenths equal to the Expansion of Air,with11° of Heat,on4016.8 Feet, the Height of the upper Barometer, with the Temperature of 31°.24, according to the 2d Table.