227 



Spatangus Colombianus. Sp. ovato-cordatus, gibbus, convexus, 

 antice planulato; ambulacris quinis, lanceolatis, transversim punc- 

 tatis. 



Terebratula Tayloriana. Testa triangulari, sulcis Iongitudinali- 

 bus impressis ; valva inferiore in superiorem reflexa ; margine bipli- 

 cato. 



Terebratula Poeyana. Testa elongato-ovata, Isevi, inflata; nate 

 producta, incurva; foramine submagno. 



Tellina [?] Humboldtiana. Testa scalenia, inflata, antice trun- 

 cate ; striis transversis, elevatis, remotiusculis, rotundatis. 



The Committee, consisting of Dr. Patterson, Prof. Bache, 

 and Mr. Walker, to whom was referred a paper, entitled, "On 

 the Insufficiency of Taylor's Theorem as commonly investi- 

 gated, with Objections to the Demonstrations of Poisson and 

 Cauchy, and the assumed Generalization of Mr. Peacock; to 

 which is added, a New Investigation and Remarks on the De- 

 velopment and Continuity of Functions, by Charles Bonny- 

 castle, Professor of Mathematics in the University of Virgi- 

 nia," reported in favour of its publication in the Transactions 

 of the Society, which was ordered accordingly. 



The paper of Professor Bonnycastle is composed of three sections. 

 In the first, which is on the "Development of Functions," he points 

 out and discusses what he considers to be " the errors and conflicting 

 views resulting from the vague manner in which mathematical writers 

 have usually conceived the ultimate object of their peculiar logic." 

 The second section is on the " Continuity of Functions," and the di- 

 vision of this continuity into classes; a subject heretofore touched upon 

 only incidentally by other writers. The principal object of the paper 

 is presented in the third section, which treats of "Functions consi- 

 dered in the order of their magnitude," and particularly of "Taylor's 

 Theorem;" and the author discusses this subject with the care de- 

 manded by a theorem which forms the basis of the differential and 

 integral calculus, and which acts so important a part in all the higher 

 mathematics. 



Mr. Walker, from the Committee on making and collecting 

 observations of Celestial Phenomena, reported, in part, that 

 they had received observations of Lunar Occultations of the 

 Fixed Stars, which are given in the mean time of the respec- 



D 



