40 M. G. Kirchhoff on the Relation of the Lateral Contraction 

 taking into account equations (6) and (7), 



(Y')=£'-2C-iL 



r 



(X") = «»-2c4> 

 7 



(Y") = £"-2ciL 

 7" 



Taking now equations (11), and placing for 7* and 7" the 

 approximate values, 



_ 1 _(X / -^ + ( Y / -//) 2 



8C 2 



'-1- 



- 77 _ (X"-,Y+(Y"-6y 

 7 8C^ a 



which are obtained from equations (10), and neglecting further 

 small values of higher order, we obtain 



(X')=X'+(X'- fl ')F, 



(Y') = Y'+(Y' -b') F, 



(X")=X"-h(X"-a")Y", 



(Y")=Y" + (Y r "-Z>")F", 

 where 



F ' ! — o4[l I, - a ') , +( TLi ') ! - 3 K x '- i ') i +P- i, ) ! ] 



+ (ys+4(?'-«')) (X'-F)+| S (X''-X»)] 



F"=^+g^ 2 [(r'-«") 2 +(Y"-J") 2 -3[(X"-«") 2 + (Y"-6") 2 ] 



-| s (X'-X f )-(^-4(f'-«"))(X''-X n )]. 



The observations made are calculated according to these formulae. 

 Of the magnitudes occurring in them, X', Y r/ , X /; , Y 7 ', X', Y ! , 

 X", Y" were obtained directly from readings of the images of 

 the scale ; a!, b', a", b" fiom the measured distances of the 

 plummets i, i (fig. 2, Plate I.), and of two plummets formed 

 of the threads f, f; f — a! and %" — a" were measured with a 

 circle. There only remains for further discussion the manner 



and 



