1825.] 



Barometrical Measurement of Heights. 



S7, 



barometer — a circumstance that cannot fail to vitiate the calcu- 

 lation of the altitude. 



Correction for Latitude, 



Hitherto We have considered the earth as a sphere at rest, but 



if we admit that it revolves on its axis, then would its figure, 



supposing it to have been originally a fluid mass, become that 



of a spheroid flattened at the poles, and protuberant at the 



equator. 



If 



placed 



■ -JL 





iiu^iM 



withiii me earth that the one branch shall extend from its surface 

 at the equator EE to the centre, and that the other shall protrude 

 to the surface at either pole PP, then will the density of the 

 mercury within the branch at the equator, diminished from the 

 centrifugal force there, be inferior to its density within the 

 branch at the pole. The latter will consequently press on 

 the fluid within the rotating branch, and cause it to ascend until 

 its superior height, compensating its inferior density, produces 

 an equilibrium of pressure between the two columns; their 

 heights now being reciprocally as their mean densities. 



The surface of the earth being no longer everywhere equidis- 

 tant from the centre, we must now define the difference of level 

 of two points not situated in the same vertical line as being equal 

 to the difference of their vertical distances from the surface of 

 the earth, or rather thatof the ocean, conforming, i^, figure to 

 that of a spheroict/f ^j,^^^' ^^' ^^' 



The centrifugal force increasing with the length of the radius 

 of rotatiop, and the intensity of gravity diminishing as the dist- 



,,,f^}ice from the centre of the earth, it follows that the force of the 

 latter is least at the equator, and that the variation will diminish 



^* ?fey^;tfpf»roach the poles in the ratio of the distance of the sur- 



