Airopaidia

CHAPTER LXXIIII.

USE AND PRACTICE OF THE FOURTH TABLE, IN THE FIRST EXAMPLE.

The use.

Section 379. TO shew in Feet, and Tenths, what is the Expansion of Air on each thousand Feet, from 1000 to 9000 Feet, with each Degree of Temperature from 1 to 100 Degrees, on Farenheit’s Scale.

The practice.
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, with 11 in the left Hand vertical Column of Temperature, and (first) on 4000 Feet, along the upper Line: the Place of Meeting gives the Expansion of the Air, with 11 Degrees on 4000 Feet: viz. 106.92.⁠[126]

Next; look with 11 Degrees, and (as there is a Cypher only in the Place of Hundreds) on 10, (viz. of the 16 Feet) call the 10, a 1000; the Place of Meeting, or Answer is 26.73:

Thirdly; with 11, on 6, (viz. of the 16,) calling it 6000; the Answer is 160.38:

Fourthly; with 11, on 8, (viz. the .8,) and the Answer is 213.84.

381. Having added the respective Expansions together, thus;

with 11°, on	4016.8			Feet. Tenths.
with 11° on	4000	=	106.92	106.92
	10	=	26.73	.2673
	6	=	160.38	.16038
	.8	=	213.84	.021384
				—————
		Expansion		107.369064;

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.
	1000	2000	3000	4000	5000	6000	7000	8000	9000
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 of Thousands in the Question, (viz. 4000,) the Answer must remain, viz. 106.92, as in the Table, which is calculated for the Place of Thousands.

2. For the Place of Hundreds, 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 over one Figure or Place to the left.

3. For the Place of Tens, in the Question, (viz. 10 Feet,) the decimal Point in the Answer, must be removed over two Figures, or Places, to the left.

4. For the Place of Units, in the Question, (viz. 6) the decimal Point in the Answer, must be removed over three Figures, or Places, to the left.

5. For the Place of a Decimal, in the Question, (viz. .8) the decimal Point, in the Answer, must be removed over four Figures, or Places to the left, by adding a Cypher: and for the Place of each further Decimal in the Question;—one Place 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 first Decimal, in the Answer, is Feet 107.3 Tenths equal to the Expansion of Air, with 11° of Heat, on 4016.8 Feet, the Height of the upper Barometer, with the Temperature of 31°.24, according to the 2d Table.