PEIRCE. — THE GllAPIIICAL SUPERPOSITION OF LINES OF FORCE. 157 



If a and A satisfy the equation 



dn^ dW dV , dV 



dx- Cif dx Cij ^ ^ 



ST is of the form <? .r + /* ^ + c. 



In general a and A. must both be sohitions of an equation of the 

 form 



d-^V d'^V „ dV ^, dV 



where P and Q are any functions of x and y such that dP/dy = dQ/dx. 



The question whether if (a, /8) and (X, /*) are orthogonal pairs and 

 (a + A, /? + yn) is not an orthogonal pair, it is possible to find a func- 

 tion {B) of ^8, and a function (J/) of /x such that (a + A., ^ + M) 

 shall form an orthogonal pair, has already been answered ; for a and \ 

 must satisfy (31) in any case, and if they do this, nr may be determined 

 from (29) and (30) and B and xl/from (17) and (20). 



The Jefferson Laboratory, 



Harvard College, Cambridge, Mass. 



