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CHAPTER XVlt 



ELIMINATION OF CONSTANTS AND FUNCTIONS. 



241. WE may make use of differentiation in order to 

 eliminate from an equation involving variables and constants 

 one or more of the constants. For example, let 



(<,-&)*+ (*-a) 2 -c 2 =0 ................ (1). 



Differentiate tliree times, giving 



a = ..................... (2), 



From these four equations we may deduce an equation 

 free from the three constants : we have 



dy _ x a 

 dx~ y b ' 



(y-bf (y-b) 



dy d*y 

 y_ _ _dx_dx* _ 3c 2 (a? a) 



*- r "(i^ftT 1 " 1 



3 ' 



