62 LECTURES AND ESSAYS [1869- 



and by proper choice of axes, 



h= -h 

 k= k 

 &-W = a\ 

 Hence, 



a *y 9 



w = -- - a 2 . 

 k 



The lines become 



+ A)S 2 - 22^ - 20 2 + - Aa 2 s + 4(ky - 2 ) 2 - 4h*x* = 0. 

 If the three circles are equal, we have further, 



N/2 



Accurate drawings of this case, and of the lemniscates 

 in the case of a rectangular parallelogram, have been 

 prepared, to accompany this paper, by Messrs. Meik and 

 Brebner, in the Physical Laboratory of the University. 

 The dotted lines in these diagrams show the lines of flow 

 when the signs of a source and sink are transposed. 1 



Verifications have been sought by determining equi- 

 potential lines experimentally, and superposing them 

 upon drawings of the stream lines. The experiments 

 were executed by students in the Physical Laboratory. 

 The process employed was essentially that of Kirchhoff, 

 but the use of Thomson s galvanometers has made it much 

 more rapid, as well as more delicate. 



Spherical Surfaces. To extend the method above used 

 to spherical surfaces, we must take as starting-point, not 

 a single source, but a source and sink at the extremi- 



1 That a greater variety of curves might be given, without over 

 crowding the figure, the two sides of one of the diagrams have been 

 made unsymmetrical, some of the curves being given (in half) on the 

 one side, others on the other. 



