JURIN V. ROBINS AND PEMBERTON 147 



a limit in insisting that there are variables which 

 reach their limits. His interpretation of Newton 

 on this point appears to us more nearly correct than 

 that of Robins ; Jurin's geometrie illustrations of 

 limit-reaching variable, intended to aid the imagina- 

 tion, though as he admits incapable of exhibiting the 

 process "ali the way," are nevertheless interesting 

 (see our §§ 124, 132, 133). The imagination is 

 subject to limitations where the reason is stili free 

 to act. 



Robins, and after him Pemberton, deserve credit 

 in clearly, openly, and completely breaking away 

 from infinitely little quantities, and from prime and 

 ultimate ratios. Robins's conception of a limit was 

 narrow, but this narrowness had certain peda- 

 gogical advantages, since it did not involve a mode 

 of advance to the limit which altogether tran- 

 scended the power of the imagination to follow ali 

 the way (see our §§ 117, 118, 129, 130). 



It is interesting to observe that both Jurin and 

 Robins disavow belief in the possibility of a sub- 

 division of a line into parts so as to reach a point — 

 they assert "that such subdivision can never be 

 actually finished " (see our §§ 126, 132). 



Robins discarded the use of Newton's moinents 

 in developing the theory of fluxions (see our 

 §§ 119, 120). 



Toward the end of his long debate with Robins, 

 Jurin begins to disavow infinitely small quantities. 

 He brings out the difference between infinitesimals 

 as variables, and infinitesimals as constants. He 



