SOLID GEOMETRY. 



li'"7. A surface is generated by a straight line intersecting 



the t\vu .-itruilit lines 



and A, fj. are the distances of the points where the generator meets 

 these straight lines from the points where the axis of z meets 

 them : prove that the principal radii of curvature at a point on 

 the first straight line are given by the equation 



c'p* sin* 2a - 2cp sin 2a(X- ft cos 2a)(4c' + /t sin' 2a)l 



1208. A surface is generated by the motion of a variable 

 circle, which always intersects the axis of x and is parallel to the 

 plane of yz, -If, at a point on the axis of x, r be the radius of the 

 circle and 6 the angle which the diameter through the point 

 makes with the axis of z, the principal radii of curvature at the 

 are given by the equation 



1209. A surface is generated by a straight line which always 

 intersects a given circle and the straight line through the centre 

 perpendicular to the plane of the circle ; is the angle which the 

 generator makes with the fixed straight line, and < the angle 

 which the projection of the generator on the plane of the circle 

 makes with a fixed radius : prove that the principal radii of cur- 

 vature at the point where the generator meets the fixed straight 



M 



1)' 



and that at the point where it meets the circle they are given by 

 .Aviation 



ng the radius of the circle. 



