1890 - 91 .] Lord McLaren on Glissette of Two-term Oval. 
85 
In these expressions, r is a line drawn from the tracing-point to 
the centre or origin of polar coordinates of the pedal, and a is the 
inclination of that line to the axis of the generating curve, or refer- 
ence line for its polar coordinates. 
If the angular coordinates of the generating curve and its pedal be 
of the form, cos mO, the glissette can be derived from the latter 
without expanding the quantity. Thus, if the generating curve be 
the negative-pedal of the parabola, or 
R*cos(y) = ad, (1) 
the equation of the pedal, or common parabola, is 
It cos (j^ = a* , or It • cos 2 ^y^ = a , • • (2) 
and the two equations of the glissette of (1) are by the above 
formula (III), 
(x-r- cos 6 + a)cos 2 
(y - r • sin 0 + a)cos : 
0 - \ 
rrr a 
• • ( 3 ) 
Again, if the generating curve be the parabola (2), the equation of 
the pedal is 
It cos 6 = a (4) 
and the two equations of the glissette are, by (III), 
( (x. - r cos 6 + a)cos 6 = a; 
(y - r sin 6 + a) • cos (o - = a , or (y - r • sin 0 + a) sin 0 
Note, that if the generating curve be a parabola of any degree, we 
must, in forming the 2nd equation of the glissette, substitute for 
cos (—} the value, cos , or, in the case of the common 
\nj \ n 2 / 
parabola ( - sin 0). Hence a is negative in the second of the pair 
of equations (5). 
The quantity 6 may be eliminated from the equations (5) as 
follows : — 
