1915-16.] The “ Ceometria Organica ” of Colin Maclaurin. 99 
If the equation to 0 2 R is 
y-toc = 0 ( 1 ) 
0 1 RP is given by 
bt , ,, 
y= b^ x - d) ’ 
and PQ by 
y-^ +b -w^”° (2) 
The locus of Q is therefore given by 
xy 2 -y 2 b | — ( ^ + b—A(x 3 -ax 2 ) = 0 .... (3) 
In particular : 
If l passes through 0 2 , so that a = 0, (3) reduces to the form 
If 0 2 is the foot of the perpendicular from O x on l, and l' is the line at 
infinity, the curve is the Cissoid of Diodes. 
[The Trisectrix of Maclaurin is also the particular case when V is the 
line at infinity, l perpendicular to ChC^, and cutting 0 X 0 2 in A, so that 
0 1 A = 1A0 2 ; but is not here explicitly quoted, occurring with another 
definition in the Fluxions.'] 
