38 M. G. KirchhofF on the Relation of the Lateral Contraction 

 from which is obtained 



Hence we have with reference to the equations (8), 



or, since f' = £°, 



In the same way may be obtained 





c" = C-A + ?"-?°- ^"~ a " ) 2 ( ^"~ X " ) - 

 But from equations (1) and (2) we have 



from equations (6) and (9) it follows that approximately 

 , _ X'-g 



and also 



Hence we obtain 

 p'=C+A-ic[(|,+r-«')(X'-l') + g*(X"-X'')], 



c"=C-A+ Ic[i«(X'-X?) + (§«-({" -«"))(X''-ro]. 



Let these values of c' and c" be substituted in equations (4) 

 and (5), and put for </ and <y" the approximate values 



■ (X'- a ')* + (Y'-6')* -, 



7 — X gQ2 * 



„ y-^y+(p-yy f ' ' • (10) 



7 --L gQ2 >J 



which are easily obtained from the equation (9), and from others 

 formed in a similar manner. Neglecting small members of a 

 higher order, we get then 



