ATTEMPTS AT ARITHMETISATION 239 



instead of beìng a terminus which can be attained as 

 near as we please. A little difference of algebraical 

 suppositions makes a fallacious difference of form : 

 and though the residuai analysis draws less upon 

 the disputable part of algebra than the method of 

 Lagrange, the sole reason of this is that the former 

 does not go so far into the subject as the latter." 



In the same article De Morgan speaks of Kirkby's 

 Ultimators thus : 



'* A something between Landen and D'Alembert, 

 as to principle, published in 1748, was called the 

 * Doctrine of Ultimators, containing a new Acquisi- 

 tion, etc. , or a Discovery of the true and genuine 

 Foundation of what has hitherto mistakenly pre- 

 vailed under the improper names of Fluxions and 

 the Differential Calculus. ' " 



