soap-bubble, and it
becomes thinner on approaching the centre; still Newton, as I have
said, measured the thickness corresponding to every ring, and showed
the difference of thickness between ring and ring. Now, mark the
result. For the sake of convenience, let us call the thickness of the
film of air corresponding to the first dark ring _d_; then Newton
found the distance corresponding to the second dark ring 2 _d_; the
thickness corresponding to the third dark ring 3 _d_; the thickness
corresponding to the tenth dark ring 10 _d_, and so on. Surely there
must be some hidden meaning in this little distance, _d_, which turns
up so constantly? One can imagine the intense interest with which
Newton pondered its meaning. Observe the probable outcome of his
thought. He had endowed his light-particles with poles, but now he is
forced to introduce the notion of _periodic recurrence_. Here his
power of transfer from the sensible to the subsensible would render it
easy for him to suppose the light-particles animated, not only with a
motion of translation, but also with a motion of rotation. Newton's
astronomical knowledge rendered all such conceptions familiar to him.
The earth has such a double motion. In the time occupied in passing
over a million and a half of miles of its orbit--that is, in
twenty-four hours--our planet performs a complete rotation; and in the
time required to pass over the distance _d_, Newton's light-particle
might be supposed to perform a complete rotation. True, the
light-particle is smaller than the planet, and the distance _d_,
instead of being a million and a half of miles, is a little over the
ninety thousandth of an inch. But the two conceptions are, in point of
intellectual quality, identical.

Imagine, then, a particle entering the film of air where it possesses
this precise thickness. To enter the film, its attracted end must be
presented. Within the film it is able to turn _once_ completely round;
at the other side of the film its attracted pole will be again
presented; it will, therefore, enter the glass at the opposite side of
the film _and be lost to the eye_. All round the place of contact,
wherever the film possesses this precise thickness, the light will
equally disappear--we shall therefore have a ring of darkness.

And now observe how well this conception falls in with the law of
proportionality discovered by Newton. When the thickness of the film
is 2 _d_, the particle has time to pe