eat mathematical discovery of infinite series and
fluxions--now known by the name of the Differential Calculus. He wrote
these things out and must have been quite absorbed in them, but it never
seems to have occurred to him to publish them or tell any one about
them.

In 1664 he noticed some halos round the moon, and, as his manner was, he
measured their angles--the small ones 3 and 5 degrees each, the larger
one 22 deg..35. Later he gave their theory.

Small coloured halos round the moon are often seen, and are said to
be a sign of rain. They are produced by the action of minute
globules of water or cloud particles upon light, and are brightest
when the particles are nearly equal in size. They are not like the
rainbow, every part of which is due to light that has entered a
raindrop, and been refracted and reflected with prismatic
separation of colours; a halo is caused by particles so small as to
be almost comparable with the size of waves of light, in a way
which is explained in optics under the head "diffraction." It may
be easily imitated by dusting an ordinary piece of window-glass
over with lycopodium, placing a candle near it, and then looking at
the candle-flame through the dusty glass from a fair distance. Or
you may look at the image of a candle in a dusted looking-glass.
Lycopodium dust is specially suitable, for its granules are
remarkably equal in size. The large halo, more rarely seen, of
angular radius 22 deg..35, is due to another cause again, and is a
prismatic effect, although it exhibits hardly any colour. The angle
22-1/2 deg. is characteristic of refraction in crystals with angles of
60 deg. and refractive index about the same as water; in other words
this halo is caused by ice crystals in the higher regions of the
atmosphere.

He also the same year observed a comet, and sat up so late watching it
that he made himself ill. By the end of the year he was elected to a
scholarship and took his B.A. degree. The order of merit for that year
never existed or has not been kept. It would have been interesting, not
as a testimony to Newton, but to the sense or non-sense of the
examiners. The oldest Professorship of Mathematics at the University of
Cambridge, the Lucasian, had not then been long founded, and its first
occupant was Dr. Isaac Barrow, an eminent mathematician, and a kind old
man. With him N