BIFILAR BALANCE. 65 



On the other hand, if k is the common perpendicular EE' to the 

 projection of the two wires, we have also 



(A + A/)/& = 40 sin 0, 



for the two numbers of this equation represent the surface of the 

 parallelogram DFD'F'. 



The moment Q of the couple of the forces q has the value 



(7) 



this formula reduces to the expression (5) found above, if we suppose 



p 

 h = h and /' =p , that is to say when the conditions of symmetry 



are fulfilled. 



If z is the vertical distance of the middle of the two lines which 

 join the points of support, we may put 



In like manner, remembering that the greatest value of p corres- 

 ponds to the smallest value of h, if we put 



it follows that 



h h' 42 i + e8 



and therefore 

 (8) 



As 8 is positive, it will be seen that the maximum of Q corres- 

 ponds to 8 = 0. The conditions of symmetry are therefore those 

 VOL. n. F 



