512 Royal Astronomical Society. 



space may serve for great results. In the present instance we have 

 to point out the singularities of thought which made Mr. Frend the 

 last, we should suppose, of the learned Anti-Newtonians, and a noted 

 oppugner of all that distinguishes algebra from arithmetic. Opposi- 

 tion to the theory of gravitation must in future be left to those whose 

 mechanics do not distinguish velocity from force ; and the rejection 

 of the distinctive principles of algebra to those who would teach like 

 philosophers what they have learnt like schoolboys, without going 

 through any intermediate stage. But the subject of the present me- 

 moir stands in neither of these predicaments ; and it would be highly 

 interesting in itself, and no less than due to expiring tenets, to spe- 

 cify the probable influences under which such a mind as that of Mr. 

 Frend directed him to stand quite alone among men of his philoso- 

 phical acquirements ; especially when it is considered that, up to 

 the age of thirty-six, he had been a successful teacher of those scien- 

 tific doctrines which he afterwards opposed, both by serious argu- 

 ment and ridicule*. 



Undoubtedly the prime mover of this curious change was the al- 

 teration which took place in his doctrinal views of religion. Having 

 been led to conclude that he had been betrayed by authority into 

 the belief of propositions both inexplicable and false, the tendency 

 to think that the inexplicable must be false, or at least to regard the 

 former with strong suspicion, was a necessary ingredient of his fu- 

 ture reflections on all subjects. The manner in which several leading 

 doctrines of physics and mathematics had been handled by names of 

 celebrity, was highly calculated to call out this disposition. The 

 doctrine of attraction, — a mysterious connexion between matter and 

 matter, with no existence but in its results ; the theory of quantities 

 less than nothing, a phrase which, arithmetically considered, is a 

 simple contradiction of terms, were adopted at the time when Mr. 

 Frend taught in a most positive and substantive sense, by the ma- 

 jority of investigators and all elementary writers. 



It was in vain that Newton, obviously hoping for some further 

 elucidation of his great regulator, concluded the Principia with a 

 caution that he had not yet (nondum) found out the source of gravi- 

 tation ; his successors and commentators, with one voice, pronounced 

 him the discoverer of the final mechanical cause of the planetary 

 motions ; and popular writers, who seldom refuse to say B when 

 their leaders have said A, added that Newton had found out why 

 water runs down hill. With respect to algebra, the matter was still 

 worse. Euler asserted downright that a penniless man, fifty crowns 

 in debt, has fifty crowns less than nothing ; and offered proof. He 

 assumes that a gift of fifty crowns would make this man richer ; and 



* In a magazine which lasted for a few months of 1803, ' The Gentle- 

 man's Monthly Miscellany,' of which Mr. Frend was editor, or co-editor, 

 is an article by him, entitled" Pantagruel's Decision of the Question about 

 Nothing," in which the manner of Rabelais is so well caught, that any one 

 on a first perusal would think it likely to be an actual adaptation or parody, 

 until a search through the writings of Rabelais satisfied him that it was 

 simple imitation. It is a satire against some parts of algebra. 



