488 
NOTE ON THE PROJECTION OF THE ELLIPSOID. 
[366 
respectively. Hence to the ellipse OB, OC drawing the two tangents which are parallel 
to OA, to the ellipse 00, OA the two tangents which are parallel to OB, and to the 
ellipse OA, OB the two tangents which are parallel to 00, we have on each of these 
ellipses the two points which are the points of contact therewith of the ellipse which 
is the projection of the contour section, or apparent contour of the ellipsoid ; that is, 
we know six points, and at each of these points the tangent, of the last-mentioned 
ellipse; and the ellipse in question, or apparent contour of the ellipsoid, can thus be 
traced by hand accurately enough for ordinary purposes. 
In connexion with what precedes, I may notice a convenient construction for the 
projection of a circle. Suppose that we have given the projection of the circumscribed 
square ABCD; then if we know the projection of one of the points M, i\T, P, Q, say 
of the point M, the projections of all the points and lines of the figure can be obtained 
graphically by the ruler only with the utmost facility; that is, in the ellipse which 
is the projection of the circle we have eight points, and the tangent at each of them, 
and the ellipse may then be drawn by hand. And to find the projection of the point 
M, it is only necessary to remark that in the figure the anharmonic ratio 
M, it is only necessary to remark that in the figure the anharmonic ratio 
ot the points A, M, O, G is =|(V2 — 1); hence the corresponding anharmonic ratio of 
the projections of the four points is also = (V2 — 1); and the projections of A, B, C, D, 
and consequently those of A, C, 0, being known, the projection of M is thus also known. 
Cambridge, June 15, 1865.