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 expressed 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 delF Imperiale Regio Instituto del Regno Lom- 

 hardo-Veneto. Vols. 1-5. 



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

 vol. 2, 2 Parts. 



MaxtoelVs Narrative of the Princes 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, 8(C. By W. J. Hughes, M. R. I. A. Presented 

 by the Author. 



