BAROMETRICAL LEVELLING.

36. The relative height of summits, the rate of fall of streams, and absolute elevation, within a few feet, may be easily, rapidly, and cheaply found by the barometer. This also affords an excellent check upon subsequent levelling operations. The results thus obtained depend upon the physical property, that the density of the air decreases as the square of the height.

37. The barometer is a glass tube, partly filled with mercury, having a vacuum in the upper part. By it the exact density of the air at any point is determined. Accompanying are two thermometers; one attached, showing the temperature of the barometer; the other detached, showing the atmospheric temperature.

38. Knowing now the manner of finding the density of the air at any two points, and also the relation between density and height, the operation of levelling by the barometer is very simple.

The modus operandi is as follows, (see tables A, B, C, and D):—

Let us have the notes.

	Barom.	Attached Therm.	Detached Therm.
Upper Station,	29.75	28.5	27.9
Lower Station,	26.80	36.8	36.3
	Latitude 46° N.

We have by table A, against the bar. point,	29.75,	6108.6
also by table A, against the bar. point,	26.80,	5276.6

The difference		832.0
Diff. of attached therm. 36.8°- 28.5° = 8.3°	(table B)	-12.2

		819.8

Double the sum of detached thermometers multiplied by 1 1000 of 819.8 is
2(27.9 + 36.3) × .8198 =		+ 105.3

		925.1
Correction (see table C) for lat. 46° N. and approximate height 925.1		+ 3.1

		928.2

Final correction by table D. The barometer at the lower station being 26.80, and the tabular number against 27.56 being 0.22, that for 26.80 will be 0.31, and we have

1000 to .31 as 928.2 to 0.287, or 0.3,

which add to 928.2 and we have as the final height

928.5 metres, or 928.5 × 3.28 = 3045.48 feet.

The tables above referred to, are those of Mr. Oltman, and are considered as the most convenient and reliable of any published.

English Inches.	Metres.

TABLE A.

14.56	418.5
14.61	440.0
14.65	461.5
14.68	482.9
14.72	504.2
14.76	525.4
14.80	546.6
14.84	567.8
14.88	588.9
14.92	609.9
14.96	630.9
15.00	651.8
15.04	672.7
15.08	693.5
15.12	714.3
15.16	735.0
15.20	755.6
15.24	776.2
15.28	796.8
15.31	817.3
15.35	837.8
15.39	858.2
15.43	878.5
15.47	898.8
15.51	919.0
15.55	939.2
15.59	959.3
15.63	979.4
15.67	999.5
15.71	1019.5
15.75	1039.4
15.79	1059.3
15.83	1079.1
15.87	1098.9
15.91	1118.6
15.95	1138.3
15.98	1157.9
16.02	1177.5
16.06	1197.1
16.10	1216.6
16.14	1236.0
16.18	1255.4
16.22	1274.8
16.26	1294.1
16.30	1313.3
16.34	1332.5
16.38	1351.7
16.42	1370.8
16.46	1389.9
16.50	1408.9
16.54	1427.9
16.57	1446.8
16.61	1465.7
16.65	1484.7
16.69	1503.4
16.73	1522.2
16.77	1540.8
16.81	1559.5
16.85	1578.2
16.89	1596.8
16.93	1615.3
16.97	1633.8
17.01	1652.2
17.05	1670.6
17.09	1689.0
17.13	1707.3
17.17	1725.6
17.20	1743.8
17.24	1762.1
17.28	1780.3
17.32	1798.4
17.36	1816.5
17.40	1834.5
17.44	1852.5
17.48	1870.4
17.52	1888.3
17.56	1906.2
17.60	1924.0
17.64	1941.8
17.68	1959.6
17.72	1977.3
17.76	1994.9
17.79	2012.6
17.83	2030.2
17.87	2047.8
17.91	2065.3
17.95	2082.8
17.99	2100.2
18.03	2117.6
18.07	2135.0
18.11	2152.3
18.15	2169.6
18.19	2186.9
18.23	2204.1
18.27	2221.3
18.31	2238.4
18.35	2255.5
18.39	2272.6
18.42	2289.6
18.46	2306.6
18.50	2323.6
18.54	2340.5
18.58	2357.4
18.62	2374.2
18.66	2391.1
18.70	2407.9
18.74	2424.6
18.78	2441.3
18.82	2458.0
18.86	2474.6
18.90	2491.3
18.94	2507.9
18.98	2524.3
19.02	2540.8
19.05	2557.3
19.09	2573.7
19.13	2590.2
19.17	2506.6
19.21	2622.9
19.25	2639.2
19.29	2655.4
19.33	2671.6
19.37	2687.9
19.41	2704.1
19.45	2720.2
19.49	2736.3
19.53	2752.3
19.57	2768.3
19.61	2784.4
19.65	2800.4
19.68	2816.3
19.72	2832.2
19.76	2848.1
19.80	2864.0
19.84	2879.8
19.88	2895.6
19.92	2911.3
19.96	2927.0
20.00	2942.7
20.04	2958.4
20.08	2974.0
20.12	2989.6
20.16	3005.2
20.20	3020.7
20.24	3036.2
20.28	3051.7
20.31	3067.2
20.35	3082.6
20.39	3097.9
20.43	3113.3
20.47	3128.6
20.51	3143.9
20.55	3159.2
20.59	3174.4
20.63	3189.7
20.67	3204.9
20.71	3220.0
20.75	3235.1
20.79	3250.2
20.83	3265.3
20.87	3280.3
20.90	3295.3
20.94	3310.3
20.98	3325.3
21.02	3340.2
21.06	3355.1
21.10	3370.0
21.14	3384.8
21.18	3399.6
21.22	3414.4
21.26	3429.2
21.30	3443.9
21.34	3458.6
21.38	3473.3
21.42	3487.9
21.46	3502.5
21.50	3517.2
21.54	3531.8
21.57	3546.3
21.61	3560.8
21.65	3575.3
21.69	3589.8
21.73	3604.2
21.77	3618.6
21.81	3633.0
21.85	3647.4
21.89	3661.7
21.93	3676.0
21.97	3690.3
22.01	3704.6
22.05	3718.8
22.09	3733.0
22.13	3747.2
22.17	3761.3
22.20	3775.4
22.24	3789.5
22.28	3803.6
22.32	3817.7
22.36	3831.7
22.40	3845.7
22.44	3859.7
22.48	3873.7
22.52	3887.6
22.56	3901.5
22.60	3915.4
22.64	3929.3
22.68	3943.1
22.72	3956.9
22.76	3970.7
22.80	3984.5
22.83	3998.2
22.87	4011.9
22.91	4025.6
22.95	4039.3
22.99	4052.9
23.03	4066.6
23.07	4080.2
23.11	4093.8
23.15	4107.3
23.19	4120.8
23.23	4134.3
23.27	4147.8
23.31	4161.3
23.35	4174.7
23.39	4188.1
23.43	4201.5
23.46	4214.9
23.50	4228.2
23.54	4241.6
23.58	4254.9
23.62	4268.2
23.66	4281.4
23.70	4294.7
23.74	4307.9
23.78	4321.1
23.82	4334.3
23.86	4347.4
23.90	4360.5
23.94	4373.7
23.98	4386.7
24.02	4399.8
24.06	4412.8
24.09	4425.9
24.13	4438.9
24.17	4451.9
24.21	4464.8
24.25	4477.7
24.29	4490.7
24.33	4503.6
24.37	4516.4
24.41	4529.3
24.45	4542.1
24.49	4554.9
24.53	4567.7
24.57	4580.5
24.61	4593.2
24.65	4606.0
24.68	4618.7
24.72	4631.4
24.76	4644.0
24.80	4656.7
24.84	4669.3
24.88	4682.0
24.92	4694.5
24.96	4707.1
25.00	4719.7
25.04	4732.2
25.08	4744.7
25.12	4757.2
25.16	4769.7
25.20	4782.1
25.24	4794.6
25.28	4807.0
25.31	4819.4
25.35	4831.7
25.39	4844.1
25.43	4856.4
25.47	4868.7
25.51	4881.0
25.55	4893.3
25.59	4905.6
25.63	4917.8
25.67	4930.0
25.71	4942.2
25.75	4954.4
25.79	4966.6
25.83	4978.7
25.87	4990.9
25.91	5003.0
25.94	5015.1
25.98	5027.2
26.02	5039.3
26.06	5051.2
26.10	5063.2
26.14	5075.3
26.18	5087.2
26.22	5099.2
26.26	5111.2
26.30	5123.1
26.34	5135.0
26.38	5146.9
26.42	5158.8
26.46	5170.6
26.50	5182.5
26.54	5194.3
26.57	5206.1
26.61	5217.9
26.65	5229.7
26.69	5241.4
26.73	5253.2
26.77	5264.9
26.81	5276.6
26.85	5288.3
26.89	5300.0
26.93	5311.6
26.97	5323.2
27.01	5334.8
27.05	5346.4
27.09	5358.0
27.13	5369.6
27.17	5381.1
27.21	5392.7
27.25	5404.2
27.28	5415.6
27.32	5427.2
27.36	5438.7
27.40	5450.1
27.44	5461.5
27.48	5472.9
27.52	5484.3
27.56	5495.7
27.60	5507.1
27.64	5518.4
27.68	5529.8
27.72	5541.1
27.76	5552.4
27.80	5563.7
27.84	5575.0
27.87	5586.2
27.91	5597.5
27.95	5608.7
27.99	5619.6
28.03	5631.1
28.07	5642.2
28.11	5653.4
28.15	5664.6
28.19	5675.7
28.23	5686.8
28.27	5697.9
28.31	5709.0
28.35	5720.1
28.39	5731.1
28.43	5742.1
28.46	5753.1
28.50	5764.2
28.54	5775.1
28.58	5786.1
28.62	5797.1
28.66	5808.0
28.70	5819.0
28.74	5829.9
28.78	5840.8
28.82	5851.7
28.86	5862.5
28.90	5873.4
28.94	5884.2
28.98	5894.9
29.02	5905.8
29.06	5916.7
29.09	5927.5
29.13	5938.2
29.17	5949.0
29.21	5959.7
29.25	5970.4
29.29	5981.2
29.33	5991.9
29.37	6002.5
29.41	6013.2
29.45	6023.8
29.49	6034.4
29.53	6045.1
29.57	6055.7
29.61	6066.3
29.65	6076.9
29.69	6087.5
29.72	6098.0
29.76	6108.6
29.80	6119.1
29.84	6129.6
29.88	6140.1
29.92	6150.6
29.96	6161.1
30.00	6171.5
30.04	6182.0
30.08	6192.4
30.12	6202.8
30.16	6213.2
30.20	6223.6
30.24	6234.0
30.28	6244.4
30.32	6254.7
30.35	6265.0
30.39	6275.4
30.43	6285.7
30.47	6296.0
30.51	6306.2
30.55	6316.5
30.59	6326.7
30.63	6337.0
30.67	6347.2
30.71	6357.4
30.75	6367.6
30.79	6377.8
30.83	6388.0
30.87	6398.2
30.91	6408.3
30.94	6418.5
30.98	6428.6
31.02	6438.7
31.06	6448.8

Deg.[^[4]]	Met.
TABLE B.

0.2	0.3
0.4	0.6
0.6	0.9
0.8	1.2
1.0	1.5
1.2	1.8
1.4	2.1
1.6	2.3
1.8	2.6
2.0	2.9
2.2	3.2
2.4	3.5
2.6	3.8
2.8	4.1
3.0	4.4
3.2	4.7
3.4	5.0
3.6	5.3
3.8	5.6
4.0	5.9
4.2	6.2
4.4	6.5
4.6	6.8
4.8	7.1
5.0	7.4
5.2	7.6
5.4	7.9
5.6	8.2
5.8	8.5
6.0	8.8
6.2	9.1
6.4	9.4
6.6	9.7
6.8	10.0
7.0	10.3
7.2	10.6
7.4	10.9
7.6	11.2
7.8	11.5
8.0	11.8
8.2	12.1
8.4	12.4
8.6	12.6
8.8	12.9
9.0	13.2
9.2	13.5
9.4	13.8
9.6	14.1
9.8	14.4
10.0	14.7
10.2	15.0
10.4	15.3
10.6	15.6
10.8	15.9
11.0	16.2
11.2	16.5
11.4	16.8
11.6	17.1
11.8	17.4
12.0	17.6
12.2	17.9
12.4	18.2
12.6	18.5
12.8	18.8
13.0	19.1
13.2	19.4
13.4	19.7
13.6	20.0
13.8	20.3
14.0	20.6
14.2	20.9
14.4	21.2
14.6	21.5
14.8	21.8
15.0	22.1
15.2	22.4
15.4	22.7
15.6	22.9
15.8	23.2
16.0	23.5
16.2	23.8
16.4	24.1
16.6	24.4
16.8	24.7
17.0	25.0
17.2	25.3
17.4	25.6
17.6	25.9
17.8	26.2
18.0	26.5
18.2	26.8
18.4	27.1
18.6	27.4
18.8	27.7
19.0	28.0
19.2	28.2
19.4	28.5
19.6	28.8
19.8	29.1
20.0	29.4

[4]. The degrees refer to the centigrade thermometer.

Approximate Height.	0°	15°	40°	55°

TABLE C.

200	1.2	1.0	0.6	0.4
400	2.4	2.2	1.4	0.8
600	3.4	3.2	2.0	1.2
800	4.5	4.3	2.8	1.7
1000	5.7	5.3	3.4	2.2
1200	7.0	6.4	4.2	2.6
1400	8.2	7.6	4.8	3.0
1600	9.2	8.8	5.6	3.4
1800	10.4	9.8	6.3	3.8
2000	11.6	11.0	7.0	4.2
2200	12.8	12.1	7.6	4.6
2400	14.0	13.3	8.4	5.1
2600	15.2	14.4	9.2	5.6
2800	16.5	15.6	10.0	6.2
3000	17.7	16.8	10.8	6.6
3200	10.1	18.0	11.5	7.0
3400	20.5	19.3	12.4	7.7
3600	21.8	20.4	13.4	8.2
3800	23.1	21.6	14.3	8.7
4000	24.6	22.9	15.1	9.4
4200	25.9	24.3	15.9	10.1
4400	27.5	25.8	16.9	10.8
4600	28.9	27.1	18.0	11.5
4800	30.4	28.4	19.0	12.1
5000	31.8	29.8	19.9	12.7
5200	33.0	31.0	20.8	13.3
5400	34.3	32.4	21.7	13.9
5600	35.7	33.7	22.6	14.5
5800	37.1	35.0	23.6	15.1
6000	38.5	36.3	24.6	15.7

Barometrical Height	Metres
TABLE D.

15.75	1.71
17.72	1.39
19.68	1.11
21.65	0.86
23.62	0.63
25.59	0.42
27.56	0.22
29.53	0.03

BAROMETRICAL LEVELLING.

CHAPTER II.SURVEY.

CHAPTER II.
SURVEY.