Barometer applied to the Measurement of Heights. 361 





The best means of determining the coefficient of this 



mg 



formula, is to make use of a height (or rather a number of 

 heights), well known by actual measurement, or by trigonomet- 

 rical operations. We then substitute for h this known value, 

 and for w, w/, T, T X , the lengths of the barometrical columns, and 

 the temperature of the air at the two stations respectively, and 

 for R the mean radius of the earth, namely 348 1 280 fathoms. We 



shall thus have an equation from which the value of is read- 



mg 



ily deduced once for all. Taking the mean result of a great 

 number of observations conducted with the greatest care, by M. 



Ramond, we find , for the latitude of 46, t equal to 1 8336 J 



metres, or 10026 English fathoms. This is on the supposition 

 of a temperature of 32, and agreeably to what has been said, it 

 may be increased or diminished by adding or subtracting | 

 or a 0,00223 part for each degree above or below 32 Q . We 

 can therefore reduce it to 10000, instead of 10026, by supposing 

 the temperature somewhat lower. Thus, since 26 is 0,0026 of 

 10000 



0,00223 : 0,0026 : : 1 : 1,16. 



If, therefore, we subtract 1, 16 from 32, we shall have 30,84 

 or 31 nearly, for the temperature at which the constant coeffi- 

 cient is 10000 fathoms. 



473. Since this coefficient contains g, it must vary with g, 

 that is, with the latitude. Now, according to the law of the va- 



t This coefficient was actually determined for the latitude of 

 about 43. But the correction for small distances in latitude is so 

 inconsiderable, that it may be regarded ~as nothing. Moreover, the 

 coefficient, if corrected at all, would require to be diminished, and 

 it is thought on the whole less liable to error by excess than by de- 

 ficiency. 



| The coefficient deduced theoretically from the relative densi- 

 ties of mercury and air, as determined by Biot and Arago, allowance 

 being made for humidity, is 18334,1 metres, differing less than 2 

 metres, that is, less than 2 X 39,371 inches from the above, 

 Mech. 46 



