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 perform, two complete rotations within the film; when the thickness is 3 d, three complete rotations; when 10 d, ten complete rotations are performed.  It is manifest that in each of these cases, on arriving at the second surface of the film, the attracted pole of the particle will be presented.  It will, therefore, be transmitted; and, because no light is sent to the eye, we shall have a ring of darkness at each of these places.

The bright rings follow immediately from the same conception.  They occur between the dark rings, the thicknesses to which they correspond being also intermediate between those of the dark ones.  Take the case of the first bright ring.  The thickness of the film is 1/2_d_; in this interval the rotating particle can perform only half a rotation.  When, therefore, it reaches the second surface of the film, its repelled pole is presented; it is, therefore, driven back and reaches the eye.  At all distances round the centre corresponding to this thickness the same effect is produced, and the consequence is a ring of brightness.  The other bright rings are similarly accounted for.  At the second one, where the thickness is 11/2_d_, a rotation and a half is performed; at the third, two rotations and a half; and at each of these places the particles present their repelled poles to the lower surface of the film.  They are therefore sent back to the eye, and produce there the impression of brightness.  This analysis, though involving difficulties when closely scrutinised, enables us to see how the theory of fits may have grown into consistency in the mind of Newton.