264 NEW MODE OF REPRESENTING, ETC. 



where, ?^Lf = ^ and ^JL? = «' and ?^ = B' 



c c c 



Many more examples might be given, but we 

 think that the above will be sufficient to illustrate 

 the application of the general formulae, which have 

 been investigated in the former part of this paper. 

 The methods proposed by Dr. Peacock, Dean of 

 Ely; Fourier; M.Libri, and Murphy, to represent 

 discontinuity, are given by Dr. Peacock in his 

 well known and able Report, on the recent progress 

 and present state of certain branches of analysis, 

 made to the British Association for the advance- 

 ment of science, Cambridge, 1B33. 



