268 



Anniversary Meeting. 



[Nov. 30, 



The author considers what he has found as the weakest part of a dome 

 to be the position in which an iron belt must be placed to produce the 

 greatest effect in counteracting the thrust of the dome. If this be done, 

 the thickness of the pier may be considerably diminished, and need not 

 greatly exceed the strength necessary for supporting the superincumbent 

 weight acting vertically downvv^ards. 



III. ^"^A Supplementary Memoir on Caustics.^^ 

 By A. Cayley, E.R.S. Eeceived November 15, 1866. 



(Abstract.) 



It is near the conclusion of my " Memoir on Caustics/' Phil. Trans, 

 vol. cxlvii. (1857), pp. 2/3, 312, remarked that for the case of parallel rays 

 refracted at a circle, the ordinary construction for the secondary caustic 

 cannot be made use of (the entire curve wo aid in fact pass off to an infinite 

 distance), and that the simplest course is to measure off the distance ^GQ 

 from a line through the centre of the refracting circle perpendicular to the 

 direction of the incident rays. The particular secondary caustic, or ortho- 

 gonal trajectory of the refracted rays, obtained on the above supposition 

 was shown to be a curve of the order 8 ; and it was further shown by con- 

 sideration of the case (wherein the distance GQ is measured off from an 

 arbitrary line perpendicular to the incident rays), that the general secondary 

 caustic or orthogonal trajectory of the refracted rays was a curve of the 

 same order 8. The last-mentioned curve in the case of reflexion, or for 

 ju= — 1, degenerates into a curve of the order 6; and I propose in the 

 present supplementary memoir to discuss this sextic curve ; viz. the sextic 

 curve which is the general secondary caustic or orthogonal trajectory of 

 parallel rays reflected at a circle. 



November 30, 1866. 

 ANNIVERSARY IMEETING. 

 Lieut. -General SABINE, President, in the Chair. 



Dr. Gladstone, on the part of the Auditors of the Treasurer's Accounts 

 appointed by the Society, reported that the total receipts during the past 

 year, including a balance of 5615 9s. carried from the preceding year, 

 amounted to 564295 I6s. lid. j and that the total expenditure in the same 



