238 



than any which the writer has elsewhere seen, but also to 

 present that theorem, and many others analogous thereto, 

 under a greatly generalized form, deduced from the principle 

 of fluctuation. Functions more general than sines or cosines, 

 yet having some correspondent properties, are introduced 

 throughout ; and constants, distinct from the ratio of the cir- 

 cumference to the diameter of a circle, present themselves in 

 connexion therewith. And thus, if the intention of the writer 

 have been in any degree accomplished, it will have been 

 shown, according to the opinion expx-essed in the remarks 

 prefixed to this paper, that the development of the impor- 

 tant principle above referred to gives not only a new clear- 

 ness, but also (in some respects) a new extension, to this de- 

 partment of science. 



DONATIONS. 



Memorie delV Imperiale Regio Instituto del Regno Lom- 

 hardo-Veneto. Vols. 1-5. 



Memorie delV Instituto Nazionaleltaliano. Vol. 1 , 4 Parts, 

 vol. 2, 2 Parts. 



Maxwell's Narrative of the Prince's Expedition. (1745). 

 Published by the Maitland Club. Presented by John Smith, 

 Esq., Secretary M. C. 



Bibliotheca Scoto-Celtica. By John Reid, Esq. Pre- 

 sented by the Author. 



Hints for the better Construction of Dwellings for small 

 Farmers, %c. By W. J. Hughes, M. R. I. A. Presented 

 by the Author. 



