1865.] Mr. Cayley on Tschirnhausen' s Transformation. 541 



" 2. Whether any, and what steps should he taken for arranging, tabu- 

 lating, publishing, or otherwise making use of such data. 



"3. "Whether it is desirable to continue Meteorological Observations 

 at Sea ; and if so, to what extent, and in what manner. 



" 4. Assuming that the system of Weather Telegraphy is to be con- 

 tinued, can the mode of carrying it on and of publishing the results be 

 improved ? 



" 5. What Staff will be necessary for the above purposes? 

 " I have the honour to be, Sir, 



" Your obedient Servant, 



" J. EMERSON TENNENT." 



" The President of tlie Royal Society."" 



[The President replied to this letter, and forwarded the name of Mr. 

 Francis Galton, F.E.S., selected by the Council to be a Member of the 

 Committee.] 



December 7, 1865. 



Dr. WILLIAM ALLEN MILLER, Treasurer and Vice-President, 



in the Chair. 



It was announced from the Chair that the President had appointed the 

 following Members of the Council to be Vice-Presidents : 

 The Treasurer. 

 Mr. Gassiot. 

 Sir Henry Holland. 



Mr. Alfred Tennyson, Poet Laureate, and Mr. Robert Grant, were 

 admitted into the Society. 



The following communications were read : 



I. "Addition to the Memoir on Tschirnhausen's Transformation/' 

 By ARTHUR CAYLEY, F.R.S. Received October 24, 1865. 



(Abstract.) 



In the memoir "On Tschirnhausen' s Transformation," Phil. Trans. 

 vol. clii. (1862) pp. 561-568, 1 considered the case of aquartic equation : 

 viz. it was shown that the equation 



(a, b, c, d, ej^x, l) 4 =0 

 is, by the substitution 



transformed into 



(1, 0, C, 23, <tjj/, l) 4 =0, 



where (C, S, <) have certain given values. It was further remarked 

 that (C, J3, <) were expressible in terms of U', H', <&', invariants of the 

 two" forms (*, b, c, d, eJX, Y) 4 , (B, C, Dpf, -X) 2 , of I, J, the inva- 



2s2 



