1893.] On Operators in Physical Mathematics. 115 



Probable Satisfaction of Numerical Equivalence by Initial Convergence 

 within a certain Range for n, viz., n = ^ to + 1. 



35. Thus, n = -i in (37), (38) produces 

 a 1.5 



or* / 1 1 2 5 2 1 2 5 2 9 2 



' = BV 1+ ^ 



Here take x = 4. Then 



(50 ) 



This was the test case which failed, the error arising from the 

 numerical equality of two consecutive terms, and then, a little later, 

 of another two consecutive terms, which caused a skipping. I now 

 make 



1-0216 

 u = 0-5880, v = ^ -3- 



Their equivalence requires that 



1 0-5880 X 1-4142 



Ef= -- =' 814 ' 



which is about right. 

 When x = 2, we have 



giving n = 0-706, =----; 



1 

 which requires . y = 0'803. 



And when x = 1 we have 



r 2 



