134 LIMITS AND FLUXIONS 



he exercised in this controversy of offering poetry 

 (usually in Latin) for the sake of readers who are 

 under necessity /'of exercising their faith, rather 

 than their reason in this dispute," for ** A verse 

 may catch him, who a sermon flies, " and for the 

 sake of enlivening the subject for others, ''who 

 are judges of the dispute." 



140. In this December " Appendix " Jurin then 

 contributes A Reply to Dr. Pemberton's Postscript^ 

 which takes up 31 pages. Referring to Newton's 

 Lemma i, Jurin says that in his former expres- 

 sion, the quantities "come nearer to equaUty 

 than to bave any assignable difference between 

 them," it never was his intention to assert "that 

 during the time of the approach, the difference 

 between the quantities is not always assignable " ; 

 he meant "that, though they shall always bave a 

 difference during the finite time, yet, before the 

 end of that time, their difference shall become 

 less than any quantity that can be assigned. And 

 if my words are taken in this sense, the Dr. 's 

 objection immediately falls to the ground " (p. (24)). 

 Mr. Jurin then gives a " demonstration " of the 

 foUowing proposition : " If two lines (i) tend con- 

 stantly to equality with each other, (2) during any 

 finite time, as, for instance, an hour; (3) and thereby, 

 their difference become less than any quantity that 

 can be assigned, (4) before the end of the hour ; 

 then, at the end of that finite time, or at the end 

 of the hour, the lines will be equal." As to Dr. 

 Pemberton's charge that Jurin misinterprets Newton's 



