96 Proceedings of the Royal Society 
Take, for example, the case when S - 2u, S - 2v are equal circles. 
Then ¥ + k 2 = li 2 -f k* , 
and by proper choice of axes, 
h = - h' 
k = V 
¥ - ¥ = a 2 . 
Hence, 
The lines become 
( 1 + A)S 2 - 2(2 ky - 2a 2 + ^ + 4 (ley - a 2 ) 2 - ihV = 0. 
If the three circles are equal, we have further, 
¥ + ¥ = 2 a 2 
k — 
V2 
Accurate drawings of this case, and of the lemniscates in the 
case of a rectangular parallelogram, have been prepared, to accom- 
pany 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.* 
Verifications have been sought by determining equipotential 
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 spheri- 
* That a greater variety of curves might be given, without overcrowding 
the figure, the two sides of one of the diagrams have been made unsym- 
metrical, some of the curves being given (in half) on the one side, others on 
the other. 
