his efforts to simply lengthening the focal length of
his telescopes, however, but also added to their efficiency by inventing
an almost perfect achromatic eye-piece.

In 1663 he was elected a fellow of the Royal Society of London, and in
1669 he gave to that body a concise statement of the laws governing the
collision of elastic bodies. Although the same views had been given by
Wallis and Wren a few weeks earlier, there is no doubt that Huygens's
views were reached independently; and it is probable that he had
arrived at his conclusions several years before. In the Philosophical
Transactions for 1669 it is recorded that the society, being interested
in the laws of the principles of motion, a request was made that M.
Huygens, Dr. Wallis, and Sir Christopher Wren submit their views on the
subject. Wallis submitted his paper first, November 15, 1668. A month
later, December 17th, Wren imparted to the society his laws as to the
nature of the collision of bodies. And a few days later, January 5,
1669, Huygens sent in his "Rules Concerning the Motion of Bodies after
Mutual Impulse." Although Huygens's report was received last, he was
anticipated by such a brief space of time, and his views are so clearly
stated--on the whole rather more so than those of the other two--that we
give them in part here:

"1. If a hard body should strike against a body equally hard at rest,
after contact the former will rest and the latter acquire a velocity
equal to that of the moving body.

"2. But if that other equal body be likewise in motion, and moving
in the same direction, after contact they will move with reciprocal
velocities.

"3. A body, however great, is moved by a body however small impelled
with any velocity whatsoever.

"5. The quantity of motion of two bodies may be either increased or
diminished by their shock; but the same quantity towards the same part
remains, after subtracting the quantity of the contrary motion.

"6. The sum of the products arising from multiplying the mass of any
hard body into the squares of its velocity is the same both before and
after the stroke.

"7. A hard body at rest will receive a greater quantity of motion
from another hard body, either greater or less than itself, by the
interposition of any third body of a mean quantity, than if it was
immediately struck by the body itself; and if the interposing body be a
mean proportional between the other two, its action upon the quiescent
body w