274 DEVELOPMENT of a certain 



redudion, our two laft fluxionary equations may be otherwife 

 exprefled, thus : 



I +«' 



, , ^ (pC0f2(p'. 



Let us, for the prefent, denote the fluents of the fluxions 

 ■which enter thefe two equations, as follows : 



^-V.-.'finV' 7v/i-^'fi'i'i?"^ 



and the relation of the fluents will be exprefled thus : 

 P=(i + OP'» 



N 



2 *^ ^^ 2 2.2 ^ 



4. Now, remarking that thefe two equations have bqen obtain- 

 ed, by afluming 



, _ ^1 _j» , fin ip fi aay 



g' = I + ^r:::.-.'" ' ^"^ "" ^^ - v/ i + .'• + 2.' coi-2. « - (i + o ^/i -t' fin-^' 

 let us farther afliume two fimiiar equations, thus, 



where it is evident that when q> = o, qf' is alfo — o, and that 

 while <p or <p' increafes from o to |, (p* will alfo increafe from o 



to I- 



If we take the fluxions of this fecond aflumed equation, and 

 Teafon in all refpeds as in Article 3., we ihall arrive at a fimilar 



conclufion, that is, putting V" for /-;===ll===v, , and N" for 



7'^ ^■'fin'4'?/ . 



P' = 



