If P' be the point where P M meets Q R, we note the following
relationship of P' to P.
1. If P moves along a horizontal line, O B remains unchanged, and,
therefore, Q R or P' must move in the straight line Q R parallel to O
B.
2. If P moves along a vertical line, P' does not change, but Q R turns
round it, remaining parallel to O B.
[Illustration: FIG. 1, 2, 3]
Without taking the trouble, as I ought to have done, to inquire what
previous investigations had achieved in this matter, I thought, three
years ago, I could get an apparatus to save me the trouble of drawing
sum curves, made somewhat after the following fashion.
P (Fig. 2) is the guide or point to be taken round the primitive. It
is attached to a block, D, which works along the bar, B C, which in
its turn moves on the four wheels, e e f f, upon the frame R S U T
fixed upon the drawing board. O A is fixed perpendicular to R U, and
is such that O may be fixed at various points to determine the polar
distance. O B D is a light bar passing freely through B and forming
one side of a parallel ruler of two or more points, g g, h h, i i.
Along i i is a slot and in this works a loaded block containing a
wheel P', whose plane is always parallel to i i.
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