165 
of Edinburgh, Session 1875-76. 
When A, the fulcrum, lies without the rhombus, the cell is called 
a positive cell ; when it falls within, the cell is negative. 
The following results can easily be verified : — 
(1.) APC is a straight line. 
(2.) AP . AC is a constant quantity (Euclid III. 36), N being 
at every moment the centre of a circle with a radius NP or NC. 
This result is expressed 
by saying that the 
curves described by P 
and C are tbe inverse 
of one another. Now 
the inverse of a circle 
is generally another A 
circle. If, then, one of 
the poles of the cell be 
made to revolve in a 
circle round B, the 
other pole will describe 
a circle. There is however an exception, for when the fulcrum is 
in the circumference of the circle described by P or C, the other 
pole describes a straight line. 
The following is the geometrical proof : — 
Let the positions of P be p v p 2 , p 3 , &c., and the corresponding 
positions of C, c v c 2 , c 3 , &c. ; and suppose that the initial position 
of the system is when AC lies along the axis of x , that is, in a 
straight line with the centres A and B. Join P and p l ; C and c r 
Join the corresponding pairs P p 2 , Cc 2 , &c. 
ByEucl. II.: 12. AM 2 = MP 2 + AP 2 + 2AP • PK 
Am 2 = mp 2 + Ap 2 + 2 A p * pk 
.-. AP [AP + 2PK] = A p [Ap + 2 pk] 
AP • AC = Ap * Ac. 
AP Ac 
° r Ap ~ AC 
In the triangles APp and ACc the angle A is common ; and the 
sides about it are proportional, viz., 
AP : Ap : : Ac : AC 
