86 Calculation of Heights, determined by Barometrical Measurement. 
Given the height of the column of mercury at two stations, with the temperature 
both of the air and of mercury ; the former being shown by the detached, the lat. 
ter by the attached thermometer. Required the difference of level of the two 
stations. 
It is first necessary, if the columns of mercury be not of the same temperature, 
to reduce them to it. This is done by adding to the colder, or subtracting from the 
warmer TB of its length for every degree of difference between the attached 
thermometers*. 
The columns being reduced to the same temperature, the calculation of the dif. 
ference of level is sufficiently easy, by attending to the following practical rule. 
1st.— Take half the difference of the columns, and remove the decimal point fire 
places to the right, adding as many ciphers as may be necessary. Divide by the 
sum of the columns f, the quotient is the approximate difference of level ia 
English feet. 
2dly — Divide the sum of the columns by the difference, rejecting lOOths and 
lOOOths of inches. With the quotient, divide continually the approximate height 
found as above, reserving the alternate quotients, i. e. the 2d. 4th. 6 th. &c. 
Then these quotients divided by the odd numbers 3. 5. 7, &c. give the 1st. 2d. 3d. 
&c. corrections which are in every case additive to the approximate height 
3dly — Correct the result thus found for the temperature of the air in the fob 
ing manner. From the sum of the detached thermometers, subtract 16° 3, mul- 
tiply the approximate height by this remainder, and divide by 1000 J. The quo- 
tient increased by T y of itself is the correction for the temperature of the air : it is 
additive. If we wish to be scrupulously accurate, we may subtract from this cor- 
rectiou of itself. 
Remarks. 
This rule will give the difference of level with the same degree of precision as 
the logarithmic calculation, by attending to the corrections mentioned in the second 
part of it. lu barometrical measurement, however, it would seem to be expecting 
more accuracy than the method is capable of, in the present state of our informs, 
tion, to be solicitous about such small differences as 10 or 12 feet. This being the 
case, the 2d part of the rule may be safely disregarded, in the calculation of heights 
that do not exceed 4 or 5000 feet ; by which, theoperation is reduced to a division by 
three places of figures, Even in differences of level amounting to 10000 feet, 
one corx.otion will be found sufficient for every practical purpose. 
As to the 3d part of the rule it is not peculiar to this method, being equally ne- 
cessary when that by logarithms is resorted to. So that, upon the whole, to those 
not well versed in the use of those numbers, this method may be preferable. Cer- 
tamly, for small elevations, it seems both shorter and easier. 
Perhaps I should not omit to mention, that I have taken the rate of expansion 
L” a . lr “ of . ,ts volume at 32° for each degree of Fahrenheit’s thermometer. 
This is the determination of MM. Dulong and Petit, and, it is said, of Mr. Dalton 
e f ?,tuV.nn Ga r I,USS r' i!T! t! formula is vitiated by his using a co-efficient, 
equal to 450 when reduced to Fahrenheit’s scale. ° 
. 1 shal1 . n "' v take ’ as *“ example, the difference of level of the “ Pic du Midi” 
trigonometrically by M. Ramond and barometrically bv 
Geodede Dang0S ’ * l' arllcula ™ of which may be seen in Puissant’s 
Barometer summit of the Peak. 
Do. at M. Dangos. 
Metres , 
.537203 
.735581 
Temp. Merc. 
49.5 (F.) 
65.6 
Diff. 16.1 
Temp, of air. 
39.2 
66 4 
Sum 105.6 
^„*,^ hi !u° P , erat , !on I s performed by prefixing two ciphers and the decimal 
point to the height of the barometer to be corrected, and multiplying- bv the diffpr- 
ence of the thermometers. The product is the correction subtractive if the baro- 
meter be the warmer. 
• great accuracy is not required, it will tend to the materiallv shorten- 
mg this division to reject lOOOths and lOOths of inches from the division Vhe error 
in heights of 10,000 feet can hardly exceed 10 feet. ^vision. Ihe error 
* This » d0Q e b y ® cre, y removing the decimal point, three places to the left. 
