2-56-6. William Thomson to H. Poincaré
In train to London Dec. 23/92
Dear Mr. Poincaré,
In writing to you this forenoon before I left Glasgow, I inadvertently said “a quarter of …” instead of “four times the focal length”.11See Thomson to Poincaré, 23.12.1892 (§ 2-56-5). Will you make the correction and kindly excuse my troubling you with it. Here is the whole affair of the periodic lense problem. Let be the distance from lense to lense, the focal length of each lense: the distance from the axis, and the inclination to the axis of the ray at mid-distance between two lenses, after it has crossed lenses. We have
which shows that when is between and the inclined ray keeps always infinitely near to the axis.22In the limiting case of , we have such that the light ray’s incidence angle is conserved in the lens system. Hence motion along the axis (in the corresponding kinetic problem) is stable. The inclination increases indefinitely if is negative, or if .
For one lense we may of course substitute a group of lenses, according to well known principles.
Yours very truly,
ALS 3p. Private collection, Paris 75017.