BERKELETS ANALYST (1734) 93 



fessor G. A. Gibson had not seen them when he 

 wrote on the Analyst controversy.^ Walton seemed 

 to have a good intuitive grasp of fluxions, but 

 lacked deep philosophic insight. He showed him- 

 self inexperienced in the conduct of controversies, 

 and did not know how to protect himself against 

 attack from a skilful adversary. 



113. It is worthy of notice that Walton ^ ex- 

 preSsed himself on the nature of limits, by claiming 

 that the limit was reached. As to the nature 

 of ''variable velocity," it is interesting to see that 

 Berkeley realised the difficulty of the concept, and 

 probably saw that there was no variable velocity as 

 a physical fact, while Walton was compelled to take 

 refuge in less primitive mechanical concepts in order 

 to uphold his side of the argument. ^ Unjustiflable 

 is Walton's identification of Newton's "moment" 

 with " momentum " of mechanics. 



114. Berkeley's Lemma* was rejected by Jurin 

 and Walton. We shall see that it found no recog- 

 nition from mathematicians in England during the 

 eighteenth century, but was openly and repeatedly 

 accepted as valid in its application to limits, by 

 Woodhouse at the beginning of the nineteenth 

 century. The Newtonian derivation of the fluxion 

 of X'' (see our §§ 32, 41), accomplished by dividing 

 both and {x-\-oy'—x'^ by the finite increment 0, 

 and then putting equal to zero in the quotient, is 



^ G. A. Gibson, " The Analyst Conlroversy," in Proceedings of the 

 Edinburgh Math. Soc, voi. xvii, 1899, p. 18. 



- See our § 92. ^ See our § loS. * See our §§ 78, 92, 106. 



