ting a
value of 20. Proceed as in the first numbering and add 200. Take
For example 18 times 18.

At a glance we see six twenties plus 2 units on left hand times 2
units on right hand plus 200 equals 324.

In the fourth numbering the fingers are marked, thumbs, 21, first
fingers 22, etc., the value of the upper fingers being 20. Proceed
as in the second lumbering, adding 400 instead of 100.

[Illustration: "18 Times 18"]

Above 25 times 25 the upper fingers represent a value of 30 each
and after proceeding as in the third numbering you add 600 instead
of 200.

This system can be carried as high as you want to go, but you must
remember that for figures ending in 1, 2, 3, 4 and 5 proceed as in
the second numbering. For figures ending in 6, 7, 8, 9 and 10 the
third numbering applies.

Determine the value of the upper fingers whether they represent
tens, twenties, thirties, forties, or what. For example, any two
figures between 45 and 55, the value of the upper fingers would be
50, which is the half-way point between the two fives. In 82 times
84 the value of the upper fingers would be 80 (the half-way point
between the two fives, 75 and 85, being 80). And the lump sum to
add.

Just three things to remember:

Which numbering is to follow, whether the one described in second
or third numbering; the value which the upper fingers have; and,
lastly, the lump sum to add, and you will be able to multiply
faster and more accurately than you ever dreamed of before.

** Optical Illusions [183]

If a person observes fixedly for some time two balls hanging on
the end of cords which are in rapid revolution, not rotation,
about a vertical axis, the direction of revolution will seem to
reverse. In some experiments two incandescent "pills" of platinum
sponge, such as an used for lighting gas-burners, were hung in
tiny aluminum bells from a mica vane wheel which was turned
constantly and rapidly in one direction by hot air from a gas
flame to keep the platinum in a glow. The inversion and reversion
did not take place, as one might suppose, at the will of the
observer, but was compulsory and followed regular rules. If the
observer watches the rotating objects from the side, or from above
or from below, the inversion takes place against his will; the
condition being that the image on the retina shall be eccentric.
It takes place also, however, with a change in the convergence of
the optical axes, whether they are parallel