LettreThomson à Poincaré, 1892-12-23

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 a be the distance from lense to lense, f the focal length of each lense: yi the distance from the axis, and θi the inclination to the axis of the ray at mid-distance between two lenses, after it has crossed i lenses. We have

yi =(1-a2f)yi-1+a(1-a4f)θi-1
θi =-1fyi-1+(1-a2f)θi-1;



which shows that when a is between 0 and 4f the inclined ray keeps always infinitely near to the axis.22In the limiting case of a=4f, we have yi+1=-yi=yi-1, 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 f is negative, or if f>14a.

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.

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Thomson à Poincaré, 1892-12-23

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In writing you this forenoon before I left Glasgow ...

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fr Lettre autographe signée

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CD n° 167

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Archives Henri Poincaré

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« Thomson à Poincaré, 1892-12-23 ». La Correspondance Entre Henri Poincaré Et Les Physiciens, Chimistes Et ingénieurs. Archives Henri Poincaré, s. d, Archives Henri Poincaré, s. d, La correspondance d'Henri Poincaré, consulté le 7 février 2023, http://henripoincare.fr/s/correspondance/item/8680