1823.] the Barometer to the Measurement of Heights, 101 

 column of mercury expands -rrr^ in passing from the temperature 

 of melting ice to that of the ebullition of water, which is equiva- 

 lent to TTT^ for each degree centigrade. 



The outline which we have now given contains in an abridged 

 form all that we at present know concerning barometrical 

 measurements, their fundamental principles, and the auxiliary- 

 operations which they require. Until of late years regard was 

 only paid to a part of the conditions of the problem; the others, 

 although uaderstood, and even pointed out by distinguished 

 philosophers, remained without practical application. They 

 have been all united for the first time in the excellent formula of 

 M. de Laplace, a formula entirely founded on the general laws 

 of the equihbrium of fluids, and which is not less remarkable for 

 its exactness than for its generality. Geometers will find in all 

 the works recently published on the subject the demonstrations 

 and analytic developements of the propositions which I have 

 done no more than enunciate ; but it is in the " M6canique 

 Celeste,'' that minds familiarized with the most abstruse specu- 

 lations of science will be gratified in finding the theory of the 

 barometer connected withj:he immense series of physical laws, 

 which together constitute the system of the world. 



Method of Calculation. 



The formula of M. de Laplace reduced to the most convenient 

 form for calculation may be thus given : 

 Let z = the difference of elevation of the two stations. 



h = the height of the barometer, T its temperature, and t 



that of the air at the lower station. 

 h% 1% fj the same at the upper station. 

 We have then the following equation : 



z = log- (4) • 60158-39 feet . (1 + '0028371 . cos. 2 4-) 



j. 4/ represents the la- 

 titude: fl, the radius of the earth, = 20881129-44 feet: and we 

 may put in the place of «, in the second member, its approximate 

 value, namely, the second member itself without the last factor. 

 I have reason to believe that it is not easy to find another 

 mode of proceeding, or to represent the algebraical quantities 

 by a smaller apparatus of figures. Now though the calculation 

 may neither be very intricate nor very long, it will still try the 

 patience of those who have a great number of heights to calcu- 

 late at one time ; and barometrical operations are themselves of 



