Method Of Calculating Heights By The Barometer
The pressure of the atmosphere being measured by the barometer, it is evident that as the instrument is carried up a high mountain or elevated in a balloon, the length of the column must decrease as the atmospheric pressure decreases, in consequence of a stratum of air being left below. The pressure of air arises from its weight, or the attraction of gravitation upon it, and therefore the quantity of air below the barometer cistern cannot influence the height of the column. Hence it follo
Table I. is calculated from the formula, height in feet = 60,200 (log. 29·922 - log. B) + 925; where 29·922 is the mean atmospheric pressure at 32° F., and the mean sea-level in latitude 45°; and B is any other barometric pressure; the 925 being added to avoid minus signs in the Table.
Table II. contains the correction necessary for the mean temperature of the stratum of air between the stations of observation; and is computed from Regnault’s co-efficient for the expansion of air, which is ·002036 of its volume at 32° for each degree above that temperature.
Table III. is the correction due to the difference of gravitation in any other latitude, and is found from the formula, x = 1 + ·00265 cos. 2 lat.
Table IV. is to correct for the diminution of gravity in ascending from the sea-level.
To use these Tables: The barometer readings at the upper and lower stations having been corrected and reduced to temperature 32° F., take out from Table I. the numbers opposite the corrected readings, and subtract the lower from the upper. Multiply this difference successively by the factors found in Tables II. and III. The factor from Table III. may be neglected unless precision is desired. Finally, add the correction taken from Table IV.
Table I.
Approximate Height due to Barometric Pressure.
| Inches. | Feet. | Inches. | Feet. | Inches. | Feet. |
| 31·0 | 0 | 28·2 | 2475 | 25·4 | 5209 |
| 30·9 | 84 | ·1 | 2568 | ·3 | 5312 |
| ·8 | 169 | 28·0 | 2661 | ·2 | 5415 |
| ·7 | 254 | 27·9 | 2754 | ·1 | 5519 |
| ·6 | 339 | ·8 | 2848 | 25·0 | 5623 |
| ·5 | 425 | ·7 | 2942 | 24·9 | 5728 |
| ·4 | 511 | ·6 | 3037 | ·8 | 5833 |
| ·3 | 597 | ·5 | 3132 | ·7 | 5939 |
| ·2 | 683 | ·4 | 3227 | ·6 | 6045 |
| ·1 | 770 | ·3 | 3323 | ·5 | 6152 |
| 30·0 | 857 | ·2 | 3419 | ·4 | 6259 |
| 29·9 | 944 | ·1 | 3515 | ·3 | 6366 |
| ·8 | 1032 | 27·0 | 3612 | ·2 | 6474 |
| ·7 | 1120 | 26·9 | 3709 | ·1 | 6582 |
| ·6 | 1208 | ·8 | 3806 | 24·0 | 6691 |
| ·5 | 1296 | ·7 | 3904 | 23·9 | 6800 |
| ·4 | 1385 | ·6 | 4002 | ·8 | 6910 |
| ·3 | 1474 | ·5 | 4100 | ·7 | 7020 |
| ·2 | 1563 | ·4 | 4199 | ·6 | 7131 |
| ·1 | 1653 | ·3 | 4298 | ·5 | 7242 |
| 29·0 | 1743 | ·2 | 4398 | ·4 | 7353 |
| 28·9 | 1833 | ·1 | 4498 | ·3 | 7465 |
| ·8 | 1924 | 26·0 | 4598 | ·2 | 7577 |
| ·7 | 2015 | 25·9 | 4699 | ·1 | 7690 |
| ·6 | 2106 | ·8 | 4800 | 23·0 | 7803 |
| ·5 | 2198 | ·7 | 4902 | 22·9 | 7917 |
| ·4 | 2290 | ·6 | 5004 | ·8 | 8032 |
| ·3 | 2382 | ·5 | 5106 | ·7 | 8147 |
Â
Table I.—continued.
Approximate Height due to Barometric Pressure.
| Inches. | Feet. | Inches. | Feet. | Inches. | Feet. |
| 22·6 | 8262 | 18·9 | 12937 | 15·2 | 18632 |
| ·5 | 8378 | ·8 | 13076 | ·1 | 18805 |
| ·4 | 8495 | ·7 | 13215 | 15·0 | 18979 |
| ·3 | 8612 | ·6 | 13355 | 14·9 | 19154 |
| ·2 | 8729 | ·5 | 13496 | ·8 | 19330 |
| ·1 | 8847 | ·4 | 13638 | ·7 | 19507 |
| 22·0 | 8966 | ·3 | 13780 | ·6 | 19685 |
| 21·9 | 9085 | ·2 | 13923 | ·5 | 19865 |
| ·8 | 9205 | ·1 | 14067 | ·4 | 20046 |
| ·7 | 9325 | 18·0 | 14212 | ·3 | 20228 |
| ·6 | 9446 | 17·9 | 14358 | ·2 | 20412 |
| ·5 | 9567 | ·8 | 14505 | ·1 | 20597 |
| ·4 | 9689 | ·7 | 14652 | 14·0 | 20783 |
| ·3 | 9811 | ·6 | 14800 | 13·9 | 20970 |
| ·2 | 9934 | ·5 | 14949 | ·8 | 21159 |
| ·1 | 10058 | ·4 | 15099 | ·7 | 21349 |
| 21·0 | 10182 | ·3 | 15250 | ·6 | 21541 |
| 20·9 | 10307 | ·2 | 15402 | ·5 | 21734 |
| ·8 | 10432 | ·1 | 15554 | ·4 | 21928 |
| ·7 | 10558 | 17·0 | 15707 | ·3 | 22124 |
| ·6 | 10684 | 16·9 | 15861 | ·2 | 22321 |
| ·5 | 10812 | ·8 | 16016 | ·1 | 22520 |
| ·4 | 10940 | ·7 | 16172 | 13·0 | 22720 |
| ·3 | 11069 | ·6 | 16329 | 12·9 | 22922 |
| ·2 | 11198 | ·5 | 16487 | ·8 | 23126 |
| ·1 | 11328 | ·4 | 16646 | ·7 | 23331 |
| 20·0 | 11458 | ·3 | 16806 | ·6 | 23538 |
| 19·9 | 11589 | ·2 | 16967 | ·5 | 23746 |
| ·8 | 11721 | ·1 | 17129 | ·4 | 23956 |
| ·7 | 11853 | 16·0 | 17292 | ·3 | 24168 |
| ·6 | 11986 | 15·9 | 17456 | ·2 | 24381 |
| ·5 | 12120 | ·8 | 17621 | ·1 | 24596 |
| ·4 | 12254 | ·7 | 17787 | 12·0 | 24813 |
| ·3 | 12389 | ·6 | 17954 | 11·9 | 25032 |
| ·2 | 12525 | ·5 | 18122 | ·8 | 25253 |
| ·1 | 12662 | ·4 | 18291 | ·7 | 25476 |
| 19·0 | 12799 | ·3 | 18461 | ·6 | 25700 |
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Table II.
Correction due to Mean Temperature of the Air.
| Mean Temp. | Factor. | Mean Temp. | Factor. | Mean Temp. | Factor. |
| 10° | 0·955 | 35° | 1·006 | 60° | 1·057 |
| 11 | ·957 | 36 | 1·008 | 61 | 1·059 |
| 12 | ·959 | 37 | 1·010 | 62 | 1·061 |
| 13 | ·961 | 38 | 1·012 | 63 | 1·063 |
| 14 | ·963 | 39 | 1·014 | 64 | 1·065 |
| 15 | ·965 | 40 | 1·016 | 65 | 1·067 |
| 16 | ·967 | 41 | 1·018 | 66 | 1·069 |
| 17 | ·969 | 42 | 1·020 | 67 | 1·071 |
| 18 | ·971 | 43 | 1·022 | 68 | 1·073 |
| 19 | ·974 | 44 | 1·024 | 69 | 1·075 |
| 20 | ·976 | 45 | 1·026 | 70 | 1·077 |
| 21 | ·978 | 46 | 1·029 | 71 | 1·079 |
| 22 | ·980 | 47 | 1·031 | 72 | 1·081 |
| 23 | ·982 | 48 | 1·033 | 73 | 1·083 |
| 24 | ·984 | 49 | 1·035 | 74 | 1·086 |
| 25 | ·986 | 50 | 1·037 | 75 | 1·088 |
| 26 | ·988 | 51 | 1·039 | 76 | 1·090 |
| 27 | ·990 | 52 | 1·041 | 77 | 1·092 |
| 28 | ·992 | 53 | 1·043 | 78 | 1·094 |
| 29 | ·994 | 54 | 1·045 | 79 | 1·096 |
| 30 | ·996 | 55 | 1·047 | 80 | 1·098 |
| 31 | 0·998 | 56 | 1·049 | 81 | 1·100 |
| 32 | 1·000 | 57 | 1·051 | 82 | 1·102 |
| 33 | 1·002 | 58 | 1·053 | 83 | 1·104 |
| 34 | 1·004 | 59 | 1·055 | 84 | 1·106 |
Table III.
| Latitude. | Factor. | Latitude. | Factor. | Latitude. | Factor. |
| 80° | 0·99751 | 50 | 0·99954 | 20 | 1·00203 |
| 75 | 0·99770 | 45 | 1·00000 | 15 | 1·00230 |
| 70 | 0·99797 | 40 | 1·00046 | 10 | 1·00249 |
| 65 | 0·99830 | 35 | 1·00090 | 5 | 1·00261 |
| 60 | 0·99868 | 30 | 1·00132 | 0 | 1·00265 |
| 55 | 0·99910 | 25 | 1·00170 |  |  |
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Table IV.
| Height in Thousand Feet. | Correction Additive. | Height in Thousand Feet. | Correction Additive. |
| 1 | 3 | 14 | 44 |
| 2 | 5 | 15 | 48 |
| 3 | 8 | 16 | 52 |
| 4 | 11 | 17 | 56 |
| 5 | 14 | 18 | 60 |
| 6 | 17 | 19 | 65 |
| 7 | 20 | 20 | 69 |
| 8 | 23 | 21 | 74 |
| 9 | 26 | 22 | 78 |
| 10 | 30 | 23 | 83 |
| 11 | 33 | 24 | 88 |
| 12 | 37 | 25 | 93 |
| 13 | 41 | 26 | 98 |
Example 1. On October 21st, 1852, when Mr. Welsh ascended in a balloon, at 3h. 30m. p.m., the barometer, corrected and reduced, was 18·85, the air temperature 27°, while at Greenwich, 159 feet above the sea, the barometer at the same time was 29·97 inches, air temperature 49°, the balloon not being more than 5 miles S.W. from over Greenwich; required its elevation.
| Â | Feet. | ||||||
| Barometer | in Balloon |   | 18·85, | Table I. | = | 13007 | |
| " | at Greenwich |   | 29·97 | " |  | 883 | |
| Â | 12124 | ||||||
| Mean Temperature, 38°, Table II. Factor | 1·012 | ||||||
|  | 12269· | ||||||
| Latitude 51½°, Factor from Table III. | ·99941 | ||||||
| Â | 12262 | ||||||
| Correction from Table IV. | 38 | ||||||
| Â | 12300 | ||||||
| Elevation of Greenwich | 159 | ||||||
| "Balloon | 12459 | feet. | |||||
The following examples, from the balloon ascents of J. Glashier, Esq., F.R.S., will serve for practice.
2. Ascended from Wolverhampton, 18th August, 1862, at 2h. 38m. p.m.; barometer (in all cases corrected and reduced to 32° F) was 14·868, the temperature of the air 26°; at the same time, at Wrottesley Hall, 531 feet above the sea, in latitude 52½° N, the barometer was 29·46, and the temperature of the air 65°·4; find the elevation of the balloon above the sea.
Height, 18,959 feet.
3. From the same place an ascent was made 5th September, 1862, when at 1h. 48m. p.m. barometer was 11·954, air O°; at Wrottesley Hall 29·38, air 56°.
Height, 23,923 feet.
4. From the Crystal Palace a balloon ascent was made 20th August, 1862. At 6h. 47m. p.m. barometer was 25·55, air 50°·5; and at the same time at Greenwich Observatory, at 159 feet above the sea, the barometer was 29·81, air 63°.
Height, 4,406 feet.
5. From the same place an ascent was made 8th September, 1862. At 5 p.m., the balloon being over Blackheath, barometer was 25·60, and the air 49°·5, while at Greenwich, barometer was 29·92, air 66°·4.
Height, 4,461 feet.
Â
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“As the interchange of heat between two bodies by radiation depends upon the relative temperature which they respectively possess, the earth, by the rays transmitted from the sun during the day, must be continually gaining an accession of heat... Standard Barometer
<p>Fig. 3 represents a Standard Barometer on Fortin’s principle. The barometer tube is enclosed and protected by a tube of brass extending throughout its whole length; the upper portion of the brass tube has two longitudinal openings opposite ea... Standard Syphon Barometer
<p>Fig. 24 represents the most accurate form of the Gay Lussac barometer. The short limb is closed at the top, after the mercury is introduced, and a small lateral), and here illustrated (fig. 25). Fig. 25.<br> <img src="/images/fig25.jpg" alt=""> ... Standard Thermometer
<div>Fig. 36<br> <img src="/images/fig36.jpg" alt=""><br> </div> <p>The peculiarities in the construction of thermometers will be best understood by describing the manufacture of a <em>Standard Thermometer</em>, which is one of the most accurate m... Sympiesometer
<div>Fig. 32.<br> <img src="/images/fig32.jpg" alt=""></div> <p>Nevertheless the instrument now about to be described, depending upon similar principles, but scientifically constructed and graduated, is a very useful and valuable substitute for the... Syphon With Photographic Registration
A continuous self-registering barometer has been constructed, in which photography is employed. Those who may wish to adopt a similar apparatus, or thoroughly to understand the arrangements and mode of observation, should consult the detailed descr...