TKANSACTIONS OF SECTION A. 



651 



aud so finally we get S-U = liiiiitinpr torms 



^I-|[[(::)--(:;)M?)--^(»J,--J}.v=v.., 



wliere the braclieta po until wt; have s as i- iu tbe last of thuui. If Y vanish, 



n 



it is very easy to see what the criterion becomes. 

 The coefficient is 



in place of Y,^^, and we have to iso one root less, and so on for any number of coeffi- 

 cients beinp absent. 



12. On the Invariahle Plane of the Solar System. 

 By David P. Todd, 31. A. 



According to the well-known princijde of Laplace, that the sum of the products 

 formed by multiplying each planetary mass by the projection of the area described 

 by its radius vector in a given time is u maximum — y being the inclination of the 

 invariable plane to the ecliptic, and n the longitude of its ascending mode ; aud 

 having from the Micanique Celeste — 



tan y si'i TT » - 

 c 



f' 



tan y cos tt = - - 



f, c' and v" lieiug constants depending upon the elements of the planets which 

 make up the sj-stem, I determined in 1877 the position-elements of the invariable 

 plane of the solar system for the epoch 187'). All the papers relating to this 

 investigation were unhappily destroyed in the conflagration of the Walker Hall of 

 Amhurst College two years ago; and only the approximate results, on a memo- 

 randum which 1 have recently found, were preserved elsewhere. They are— 



y= r35' 



TT = 106° 10' 



Better values of some of the planetary masses are now known, and I have 

 lately repeated the determination, at) initio, employing the results of the latest avail- 

 able researches on the planetary elements, the epoch being the year 1000. 



ill 



SUBSECTIOX OF PUYSICS. 



1. Report of the Committee for facilitating the adoption of the Metric System 

 of Weights and Measures in Great Britain. — Seo Reports, p. 27. 



2. On the Colours of Thin Plates. 

 By Professor Lord Rayleigh, LL.D., F.B.S. 



3. On Clark's Standard Cells. By Professor Lord Rayleigh, LL.D., F.B.S. 



In the hope of finding a clue as to the origin of some of the minor anomalies 

 of (Jlark cells, I have made experiments upon the E. 31. F. of combinations, in 

 which two dillerent strengths of zinc amalgam take the place of the zinc aud pure 



