3 86 Mr/ lud lam on the Engine for turning Omls. 
Let amb ah (fig- 4-) be an ellipfe whofe center is c; 
draw the circumfcribed and infcribed circles as before , 
the former cutting the fecond axis produced in d, the 
latter cutting the firft axis in d, and the fecond axis in b. 
On d b as a diameter defcribe a circle cutting the firft axis 
a a in draw DQ_tuid bo^ Set off cr=d<l, j°^ n DR ? an( * 
draw dp at right angles cutting the firft axis in p, draw 
pm an ordinate to that axis, and m will be the point in 
the oval line where the angle of deviation is greateft. 
Othcrwife, upon c b produced fet off c r=bcg, join dr, and 
draw dp at right angles cutting the lecond axis in p: 
draw p m an ordinate to that axis, and m will be the point 
where the angle of deviation is greateft. 
At the maximum (when xx=—J pn =— , pm"-— » 
and tp 2 = — — • whence tp'=pmxpn. Alfo, pn, pm, tp, 
t + C 
are to each other as ca, cb, and \/ cax cb, refpe&ively. 
Therefore, - C A ~ ^b is the tangent of mtn, radius being 
? ^/a ax Bb 
unity. Alfo is the tangent of ntp ; and mtp is the 
complement of ntp : therefore mtn is twice the excefs 
of ntp, above 45°« 
