the Depression of the Mercury in the Tubes of Barometers. 7 

 and, by making, 



B ' = B "i^ = l^-|^ + &c. 



we get, ^j - aq = -i- + A'z 9 + B'z 4 + &c. 



The left side of this equation is equal to zero when t is in- 

 finite ; for a g then becomes 2 a. From this it follows that 

 A', B', &c. are evanescent both when t is equal to zero and 

 when it is infinite. The terms on the right side, except the 

 first, do not therefore increase indefinitely, but always remain 

 inconsiderable. 



dz da 



a = 1 + ^ + TST + &c - 



then, by dividing all the terms of the foregoing equation by a, 

 and introducing j for z 9 we shall get, 



. T dtt ds fedt 



Next P ut > Tdl - § " TIT '•' °" = 5C,/ = *•* 



Let a' stand for the same function of s that a is of cr, or of 

 As: then, making, 



A"=A'=-|^-^+&c. 



B " = B ' + 4 1 =-l4 i -w iS + ^ 



we shall get, 



— = — . \ — + A" A 2 . 5 3 + B"A 4 .5 4 + &c. 



sdt a { t 



The fraction — must next be reduced to a series of the y 



a 



powers of s. Now, 



and, 



