CRITICISMS BY BRITISH WRITERS 259 



secondly, the connection and naturai order of the 

 Sciences are interrupted, if we give a di^tinct and 

 independent origin to that which in fact, is a branch 

 of analysis derived from the same common stock, 

 whence ali the other branches are deduced. " Then 

 follows a sympathetic account of the foundations 

 for the calculus laid by Lagrange in his Thcorie des 

 fonctions analytiques^ ^798- In passing, the reviewer 

 remarks that ** Emerson, Stone, Simpson, Waring, 

 etc. , have published treatises on fluxions ; in none 

 of which, however, are the principles clearly laid 

 down." 



Review of a Memoir of Stockler, 1799 



222. In the same journal^ there is a review of 

 a memoir on fluxions written by the Portuguese 

 mathematician, Garcao Stockler, who modifies the 

 explanation of fundamentals by the introduction of 

 a '' hypothetical fluxion " (a uniform velocity that 

 generates a quantity equal to the real increment 

 generated during the actually variable motion), which 

 is always contained between the proper fluxions at 

 the first and second instant under consideration. 

 By diminishing the interval of time, the hypothetical 

 fluxion approaches the true fluxion more nearly than 

 by any assignable quantity. Here also, the real 

 object of consideration is the liinit. The reviewer 

 argues that the fundamental principles are not 

 new, and that the objections to Newton's fluxions 

 apply equally to those of Stockler. In a reply to 



^ Monthly Review ^ voi. xxviii, London, 1799, p. 571. 



