Sir William Rowan Hamilton on Fluctuating Functions. 321 



atlon. Functions more general than sines or cosines, yet having some correspon- 

 dent properties, are introduced throughout ; and constants, distinct from the ratio 

 of the circumference to the diameter of a circle, present themselves in connexion 

 therewith. And thus, if the intention of the writer have been in any degree ac- 

 complished, it will have been shown, according to the opinion expressed in the 

 remarks prefixed to this paper, that the development of the important principle 

 above referred to gives not only a new clearness, but also (in some respects) a 

 new extension, to this department of science. 



VOL. xrx. 2 T 



