250 NEW MODE OF REPRESENTING 



be found to be of considerable application in the 

 investigations in physical science. 



(12), Hitherto, so far as I am acquainted with 

 mathematical science, the object of mathematicians 

 has been to investigate the locus of the extremity 

 of the dependent co-ordinate, when the relation 

 between the independent and dependent co-ordi- 

 nates remains the same — or which is the same 

 thing, to examine the infinite variety of solutions 

 in a stream of continuous sequences, which may 

 be given to an indeterminate equation between 

 two variable quantities. This inquiry originated 

 with the illustrious Descartes, in his successful 

 attempt to solve the well known problem of the 

 ancient geometers ; and no advance, so far as I 

 know, on this idea has been taken by any suc- 

 ceeding mathematician. We think the inquiry 

 ought not to rest here ; and would beg to suggest, 

 to those interested in mathematical speculations, 

 that it would be desirable to investigate, not only 

 the infinite number of solutions of one indeter- 

 minate equation, but one or more solutions of 

 an infinite number of indeterminate equations. 

 To exemply this idea, it appears necessary to 

 have recourse to the ordinary geometrical mode 

 of representing the solutions of indeterminate 

 equations. 



