the Inflection, Reflection, and Colours of Light. 229 
Prop. III. The bending force is to the propelling force of 
light, as the sine of the difference between the angles of in- 
flection (or deflection) and incidence, to the cosine of the 
angle of inflection (or deflection). 
Prop. IV. The rays of light may be made to revolve round 
a centre in a spiral orbit. 
Prop. V. If the inflecting surface be of considerable extent, 
and a plane, then the curve described may be found by help 
of the 41. Prop. Book I. Principia; provided only, the propor- 
tion of the force to the distance be given. Thus, if the bend- 
ing force be inversely as the distance, the curve cannot be 
found ; for in order to obtain its equation, a curvilinear area 
must be squared, which in this case is a conic hyberbola ; the 
relation, however, between its ordinates and abscissae may be 
obtained in fluxions, thus ; yy -f- b y = a* x. 
If the force (which is most probable) be inversely as the 
square of the distance, the curve to be squared is the cubic 
hyperbola; Species LXV. genus III. of Newton's Enumera- 
tion ; and this being quadrable, the curve described by the 
light will be the parabola campaniformis pura ; Species LXIX. 
of Newton. 
If the force be inversely as the cube of the distance, the 
curve is a circular arch, and that of deflection is a conic hy- 
perbola.* If the inflecting body be a globe or cylinder, and 
the force be inversely as the square of the distance from the 
surface, then by Prop. 71. Book I. Principia, the attraction to 
the centre is inversely as the square of the distance from that 
centre ; and therefore, by Prop. 11. and 13. of the same book, 
the ray moves in an ellipse by the inflecting, and an hyperbola 
* Principia, Lib. I. Pro^. 8, 
