TRANSACTIONS OF SECTION A. 651 



and so finally we get 8 2 U = limiting terms 



+ ^[[(|H?)K(?)'^)l--j)--=---. 



where the brackets go until we have s as -J— in the last of them. If Y vanish. 



n dc nn ' 



n 



it is very easy to see what the criterion becomes. 

 The coefficient is 



[ 



v dY 



ax 



in place of Y B11 , and we have to use one root less, and so on for any number of coeffi- 

 cients being absent. 



12. On the Invariable Plane of the Solar System. 

 By David P. Todd, M.A. 



According to the well-known principle 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 a maximum — y being the inebriation of the 

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

 having from the Micanique Celeste — 



e" 



tan ysinj- = — 

 c 



c' 



tan y cos it — — 

 c 



c, c' and c" being constants depending upon the elements of the planets^ which 

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

 plane of the solar system for the epoch 1875. 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 I have recently found, were preserved elsewhere. They are — 



y= 1°35' 



n = 106° 10' 



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

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

 able researches on the planetary elements, the epoch being the year 1900. 



Subsection of Physics. 



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

 of Weights and Measures in Great Britain. — See 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 Clark cells, I have made experiments upon the E. M. F. of combinations, in 

 which two different strengths of zinc amalgam take the place of the zinc and pure 



