1 68 Algebra. 



compute the corresponding values of r. The results may be 

 arranged in the form 



y I 2 2.00O02O000I 2.0002000I 2.00200I 2.020I 2.21 

 X I I I.OOOOI I.GOOI • I.OOI I.OI I.T 



As before, let us start at x= i and give to Jx various fractional 



values and determine the corresponding values of Jr. 



The results may be arranged as before in the form 



Jy I .21 .020 I .002001 .00020001 .0000200001 



~Jx I .1 .01 .001 .0001 .00001 



An examination of this scheme shows that 



J y .21 

 when J.r=.i, then -^ = — = 2.1 



X . I 



1. < ^r, -^y -0201 



when J-r=. 01, then —— = =2.01 



Jx .01 



. Jy .002001 

 when Jjf=.ooi, then -f~= =2.001 



Jx .001 



. , Jy .00020001 



when J.r=.oooi, then — ^= = 2,0001 



Jx .0001 



, , Jy .0000200001 



when Jx=.ooooi, then — = =2.00001 



Jx .ooooi 



From the first part of the Article it appears that ~ is a var- 

 iable, and from what we have just obtained it further appears 



that as Jx is taken smaller and smaller the fraction -" - approaches 



Jx 



nearer and nearer the value 2, or in other words, it appears that 



Jy 



the fraction -^ approaches 2, /. <". 2 times i, as Jx approaches zero. 



In obtaining the result it is to be noticed that we consider .r to in- 



Qre3.se/r0m the value i, but if we let x increase b}^ various amounts, 



beginning to count the increase in x from the value 2, reasoning 



exactly as we have just done w^ould lead to the conclusion that 



Jy 



-f-_ approaches 4, /. e. 2 times 2, as Jx approaches zero. 



Again, if we begin to count the increase in x from the value 3 



Jy 

 we would be led to the conclusion that -^- approaches 6, /. e. 2 



times 3, as Jx approaches zero. 



