ROBERT HEATH v. JOHN TURNER 209 



Thing differs from that of its Notation in 

 Practice. . . . Those who desire further Satisfaction 

 as to the Nature of Fluxions, of their noble Use 

 and transcendant Excellence, may consult Mr. 

 Emerson's Doctrine of the whole Art^ which is . . . 

 the best of any. . . . Those writers will find them- 

 selves mistaken, who pretended to derive the finite 

 Ratios of Motion,or Fluxions producing Magnitudes, 

 without the previous Consideration of Incretnents, 

 which include the very Notion of what a Fluxion is. 

 This some have attempted by multiplying Quanti- 

 ties into their Velocity, and some by other Means, 

 the Result of which originally depends on incre- 

 mentai Principles, if they would consider the Matter 

 as far as it will go.'' The paper is brought to a 

 finish in the Ladies' Diary for 1747. 



Main Articles in the Controversy 



183. Over the pseudonym of " Cantabrigiensis " 

 there appeared in 1750 an un friendly review of 

 Simpson's Doctrine and Application of Fluxions.^ 

 The reviewer contended that the definition of a 

 fluxion as the ''magnitude by which any flowing 

 quantity would be uniformly increased " (see our 

 § 172) is very " odd " ; for, *'in quantities uni- 

 formly generated, the fluxion must be the fluent 

 itself, or else a part of it." Simpson's endeavour 

 to exclude *' velocity " " cannot be made intelligible 

 without introducing velocity into it. " '' Again, he 



^ Monthly Review ; or, New Literary Journal, voi. iv, London, 

 1750, pp. 129-131. 



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