488 PROCEEDINGS OF THE AMERICAN ACADEMY 



Nicholas St. John Green, and from Professor "William Ripley 

 Nichols, acknowledging their election into the Academy. 



It was voted to grant the use of the Hall of the Academy 

 on the morning of Thursday, December 12, to the Massachu- 

 setts Historical Society. 



The President called the attention of the Academy to a vol- 

 ume richly illustrated, entitled " Revision of the Echini," by 

 Alexander Agassiz. 



Alexander Agassiz then exhibited specimens of the Alber- 

 type and Woodburytype methods of photo-engraving employed 

 in illustrating his work. 



The Recording Secretary exhibited a new form of Theodo- 

 lite-Magnetometer. 



A letter was then read from Dr. Robert Amory, describing 

 some specimens of objects exposed to the fire of November 9, 

 which led to a discussion in which most of the members pres- 

 ent participated. 



Six hundred and fifty-second Meeting. 



January 14, 1873. — Monthly Meeting. 



« 



The Corresponding Secretary in the chair. 



The Corresponding Secretary read a letter from Professor 

 Diillen, of Pulkowa, acknowledging his election, as Foreign 

 Honorary Member, into the Academy. 



Professor J. M. Peirce read the following paper by Professor 

 J. M. Rice of Annapolis, and Professor W. W. Johnson of 

 St. John's College, Maryland, " On a New Method of obtain- 

 ing the Differentials of Functions, with especial reference to 

 the Newtonian Conception of Rates or Velocities." 



The fundamental conceptions which have been employed in the de- 

 velopment of the elementary theorems of the Differential Calculus 

 are four in number, namely, that of Infinitesimal Differences, that of 

 Limits, that of Derived Functions, and that of Rates or Fluxions. 



While the first and more recently the second have received greater 

 attention and more systematic development, the last, the Conception 

 of Rates, has. an important advantage in the readiness with which its 



