lloyal Irish Academy. 



537 



The author then enters into a disquisition relating to the number 

 of terras which will appear in the final derivee, and concludes this 

 first part with the statement of two general canons, each of which 

 affords as many tests for determining whether a prepared combina- 

 tion of coefficients can enter into the final derivee of any number of 

 equations as there are units in that number, but so connected as 

 together only to afford double that number, less one of independent 

 conditions. 



The first of these canons refers simply to the number of letters 

 drawn out of each of the given equations (supposed homogeneous) ; 

 the second to what he proposes to call the weight of every term in 

 the derivee in respect to each of the variables which are to be elimi- 

 nated. 



The author subjoins, for the purpose of conveying a more accurate 

 conception of his Pyramid of derivation, examples of the mode in 

 which it is constructed. 



When n = 1 there is one flat, 

 viz. 



When n = 2 there is one flat, 

 viz. 



1,2 



Let n as 3, there will be two 

 flats: 



Let n = 4, there will still be 

 two flats only : 



