372 Cambridge Philosophical Society : — 



originally denoted by 2 ; and therefore 8 x 16, =128 modes, for 

 which no figure remains in loco. This completes the investiga- 

 tion of the numbers 1, 60, 243, and 128, which together make 

 up the total number 432 of the modes of denotation of the nine 

 inflexions. 



LIV. Proceedings of Learned Societies. 



CAMBRIDGE PHILOSOPHICAL SOCIETY. 



October 26, 1863. — A communication was made by Mr. H. D. 

 Macleod " On the Theory of Banking." 



November 9. — Communications were made, by Dr. Humphry, 

 " The Results of Experiments on the Growth of the Jaw." 



By Mr. Todhunter " On a Question in the Theory of Probabilities." 



November 23. — A communication was made by Professor Challis 

 " On the Meteor of August 10, 1863." 



December 7. — A communication was made by Dr. Akin " On the 

 Origin of Electricity." 



February 8, 1864. — A communication was made by Professor 

 Liveing " On the new Metal, Thallium." 



February 22. — Communications were made by Professor Cayley 

 " On a Case of the Involution of Cubic Curves," and " On the Theory 

 of Involution." 



By Mr. Spencer " On Vitality." 



March 7. — Communications were made by Mr. Harry Seeley — 



1. " On the Significance of the Succession of Rocks and Fossils." 



2. " On Pterodactyles, and on a new Species of Pterodactylus 

 machcerorhynchus." 



April 18. — Communications were made by Mr. Rohrs "On the 

 Strains and Vibrations of Ordnance under the Action of Gun- 

 powder." 



By Professor Cayley " On the Classification of Cubic Curves," 

 and " On Cubic Cones and Curves." 



May 2. — Communications were made by Mr. Harry Seeley — 



1. "Note on Palaobalana Sedgwicki (nob.), a Whale from the 

 Oolite." 



2. " On the Fossil Birds of the Upper Greensand, Palceocolyntus 

 Barretti (nob.) and Pelargonis Sedgwicki (nob.)." 



3. " On the Osteology and Classification of Pterodactyles, Part II., 

 with descriptions of the new species P. Hopkinsi and P. Oweni." 



May 16. — Papers were read by Professor De Morgan — 

 1. "A Theorem relating to Neutral Series." 



The theorem is as follows. If a — a^-\-a 2 — ... be a convergent 

 series which has the limiting form 1 — 1 + 1 — ... , and if a z be of 



