DIFFERENTIAL CALCULUS. 113 



to Mathematical questions. But when Mr. De Morgan 1841. 

 began to make the application of Mathematical principles 

 to Logic, Dr. Whewell was naturally one of the first 

 to whom his ideas were communicated. In many in- 

 stances the letters were written on the occasion of sending 

 tracts to the Cambridge Philosophical Transactions. The 

 first of these, ' On the General Equation of Surfaces of 

 the Second Degree,' is dated 1830 ; 'On the Foundation 

 of Algebra,' No. I., read 1839 ; Nos. II. and III., 1843 ; 

 No. IV., 'On Triple Algebra,' 'On the Structure of 

 the Syllogism, and on the Application of the Theory of 

 Probabilities to Questions of Argument and Authority,' 

 1846. 



The work on the Differential and Integral Calculus, 1842. 

 which had been published by the Useful Knowledge 

 Society, appeared in 1842 in his complete work, a 

 closely printed octavo volume of 770 pages. The series, 

 which had commenced in the year 1836, consists of 

 twenty- five numbers, each containing thirty-two pages, 

 and to the book is added an appendix and two num- 

 bers of elementary illustrations which had been pub- 

 lished by the Society before. Of the work he says in 

 the preface : 



4 The method of publication in numbers has afforded 

 time to consult a large amount of writing on the different 

 branches of the subject; the issue of the parts has ex- 

 tended over six years, during two of which circumstances 

 with which I had nothing to do stopped all progress. The 

 first number was preceded by a short advertisement, which 

 I should desire to be retained as part of the work, for I 

 have no opinion there expressed to alter or modify, nor 

 have I found occasion to depart from the plan then con- 

 templated. 



' The principal feature of that plan was the rejection 

 of the whole doctrine of series in the establishment of the 

 fundamental parts both of the Differential and Integral 

 Calculus. The method of Lagrange, founded on a very 



