Mr.W. Spottiswoode on a Problem in Combinatorial Analysis. 349 



point where the longitudinal lines are visible. In the space be 

 a superposition of two bundles, aSb, cLd, takes place. The ray 

 Si, which belongs to the first bundle, and the other Li, of the 

 same colour, which belongs to the second, interfere with each 

 other in i under the very small angle SiL. When the ray pro- 

 ceeding from S is intercepted by the card-board, the ray iS_ is 

 absent at i, and consequently no interference occurs at this point 

 of the spectrum. 



It is really interesting to observe how every line may be caused 

 to vanish by moving the card in a proper manner before the 

 lens. From these experiments it follows, that the phenomenon 

 of the longitudinal lines is not peculiar to the spectrum, but that 

 in every case lines of interference must exist in light which has 

 passed through a convex lens. 



I therefore removed the prism, and made the slit in the 

 window-shutter wider. White light now passed through the 

 lens. By moving the plane of projection backwards and for- 

 wards, a position was at length found where the whole breadth 

 of the white image was intersected by splendid black lines which 

 crossed it horizontally. 



It is scarcely necessary to remark, that I made many experi- 

 ments to convince myself, that in the production of these lines 

 no foreign influences come into play, which, however, is suffi- 

 ciently proved by the mere inspection of them. 



L. On a Problem in Combinatorial Analysis. 

 By William Spottiswoode, M.A. ofBalliol College, Oxford*. 



THE following problem, — 

 To arrange 7 systems, each consisting of 5 ternary com- 

 binations of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 

 13, 14, 15, so that all the 15 numbers enter into each system, 

 and no combinations whatever recur ; 



Or, as it is usually stated, — 



To arrange 15 young ladies in such a manner that they may 

 walk out 3 and 3 every day in the week, no lady ever walking 

 twice with the same person, 



is well known ; but the following solution may, from its con- 

 nexion with known laws of combination, be not without in- 

 terest. I propose afterwards to notice some points respecting 

 the general case to which the present problem belongs, or more 

 strictly speaking, respecting those instances of the general case, 

 to which the method here proposed is directly applicable. 



First, to form the 35 ternary combinations, arrange the num- 

 bers as follows : — 



* Communicated by the Author. 



