374 Cambridge Philosophical Society :- — 



4. The symbol ^, the infinite of common algebra, represents an 

 extreme of infinite which can no more be attained by passage through 

 orders of infinity, than any infinite by passage from finite to finite. 



Each of these positions comes into conflict with some of the usual 

 arguments for or against the introduction of infinites. 



The second part of the paper is on the meaning of the sign of 

 equality. Mr. De Morgan contends for the ultimate attainment of 

 a purely formal algebra, in which every transformation shall have 

 meaning and validity in every possible case. He points out certain 

 difficulties and inconsistencies in the ordinary use of the sign of 

 equality, which can, he affirms, receive a consistent explanation on 

 the extension which he proposes, and which, to some extent, he con- 

 siders as virtually adopted. 



His notion is that equality, strictly so called, is but a species of the 

 genus undistinguishable ; and that the actual use of the sign ( = ) 

 shows a leaning to the generic definition. Every order of infinites 

 or infinitesimals has its own metre, and the sign (=) indicates undis- 

 tinguishability with reference to the metre, which is often in thought, 

 but for which no symbol is employed. Algebraical changes may or 

 may not demand or permit changes in the metre. It would be im- 

 possible to give any further account, with justice to the subject, in 

 a short abstract. 



3. By Mr. Harry Seeley " On Saurornia, and the Classification of 

 Pterodactyles, Part III." 



October 31, 1864. — Papers were read by Professor Selwyn " On 

 Autographs of the Sun." 



By A. R. Catton, B.A., St. Johns College, " On the Constitution 

 of Chemical Compounds." 



November 14. — A communication was made by G. F. Browne, 

 M.A., St. Catharine's College, "On certain Ice-Caverns." 



November 28. — Papers were read by Dr. Humphry on the ques- 

 tion, " Is the Vertebral Theory of the Skull to be abandoned ?" 



This communication was intended partly as a reply .to the opinion 

 expressed by Professor Huxley in his lectures on comparative ana- 

 tomy, that the vertebral hypothesis of the skull has been abolished 

 by the recent discoveries in development. Dr. Humphry commencd 

 by calling attention to the Laws of Uniformity of Plan, and Variety 

 in Detail, which prevail throughout the animal kingdom, and, indeed, 

 throughout the material system, and which the recent discoveries 

 by the microscope have shown to rule over the ultimate structure 

 and formation of all the tissues of the body. The discovery of the 

 illustration of these laws in the plan of cell-formation of the tissues, 

 and in the development of all animal and vegetable structure from 

 the simple cell-form, he regarded as the grandest discovery in phy- 

 sical science that has taken place in our time. Of late years, the 

 attention of anatomists has been much directed to the exemplifica- 

 tion of these laws in the vertebrate classes, to tracing the uniformity 

 of plan, especially in the skeleton, through the variety in detail which 



