GAUSS'S METHOD OF REDUCTION. 43 



p l no longer coincide, and neither represents the true position of 



equilibrium under the action of the same forces. The value of p 



n' 2 

 differs from / by the quantity A 2 - e-~ et \ that of /j differs from 



it by twice this quantity, and in the same direction. It follows that 



n' 2 

 the difference p^ -p gives the value of A 2 - e~* et , and that the 



position of p Q would be obtained by taking the symmetric point of p l 

 in reference to /. 



696. To determine the time of the oscillations, seven successive 

 elongations are noted, x Qt x 2 , x# x 6 on one side, and x v x 3 and x 5 

 on the other, as well as the times / , f lt . . . . / 5 , at which a division 

 near that corresponding to equilibrium passes over the cross-wire ; 

 then at the end of a given time, which it is useless to note, a series 

 of seven new elongations, x l , x\, x l 3 , are noted, and the corres- 

 ponding times of passage /J, t\ ..... 



The first series gives rise to the following table : 



Positi on of Zero. 



E,onga,ion. - 



= #0 



a A 



- X 



= a 



2 



