[Dec. 
370 Calculation of Heights from the Barometer. 
VIII. On the Calculation of Heights from Observations of the Barometer. 
To the Editor of the Gleanings in Science. 
Sir, 
The tables for calculating differences of level from barometrical observations, such 
at least as have fallen in my way, being in general spun out to such a length as to 
render them nearly as troublesome as the direct calculation from the formula ; per- 
haps you may cuusidcr the one I have now the pleasure to send you not altogether 
unworthy of a place in your Gleanings. In the first volume of the Memoirs of the 
London Astronomical Society, page 29'.). Professor Littrow has given as concise ta- 
bles as I recollect having seen any where : but they are adapted to the French mea- 
sures, anil Reaumer’s thermometer, and are, therefore, so far inconvenient. The for- 
mula he uses is, 
N^ 9436,966. (1+.002S4 cos. 2 <p) . (l-(-,0025. (<+<’) 
b‘ 
H = N. log. 
[1 +-00923 (T'— T)] b in which 
, ™ f express the height of the Barometer Temperature of the Air, and 
’ ’ I Temperature of the Mercury at the upper station. 
l > , t ' , T’ — the same at the lower station. 
<j> — Latitude of the place. 
H — Difference of level in Toises. 
Now, neglecting the factor depending on the latitude of the place, as being too 
small to he worth attending to, except perhaps in the very nicest experiments, and 
supposing the barometers at the two stations to be in the first instance reduced to 
one and the same temperature, 32° for instance*, we shall have for English feet and 
Fahrenheit’s thermometer, this simple formula. 
N = 50050 +67 ,05 (F+F') 
b' 
H = N. log. — , or iu Logarithms 
b 
Log- H = log. N +log. (log. b' — log. b) 
The following is a table of the Logarithms of N for every probable value of 
(F+F') the sum of the temperatures of the air at the two stations. 
F+F' 
Log. N. 
Diff. 
for 1° 
F+F 
Log. N. 
Diff. 
for 1°. 
60° 
70 
80 
90 
100 
110 
120 
130 
140 
4,77871 
,78353 
,78830 
,79302 
,79768 
,80229 
,80680 
,81138 
,81585 
48.2 
47,7 
47.2 
46.6 
46.1 
45.7 
45.2 
44.7 
44.3 
150° 
160 
170 
180 
190 
200 
210 
220 
4,82028 
,82166 
,82900 
83330 
,83755 
,84176 
,84593 
,85007 
43,8 
43.4 
43.0 
42.5 
42.1 
41,7 
41,4 
An example can hardly be necessary, except to show that the table gives the same 
results as other methods. Let us take the one given in No. 3 of your Gleanings, page 
87 : the two barometers reduced to the same temperature are : 
5’:=, 7344 log. = 9,86593 
4 =,5372 log. = 9,730115 
log 4’ = log. 4 —,13579 
log. ,13479 = 9,13287 
for F+F’ = 105. o 6 the table gives 4,80029 
Feet 8573-5 u= 3,93316 
* A table for this correction, of limited extent, however, will be found in Daniel’s 
Meteorological Essays, 2d ed. p. 372. 1 have extended it so as to be useful to the 
residents iu mountainous regions, and perhaps you may think it worth printing. 
