July 11, 1919] 



SCIENCE 



41 



DISCUSSION AND CORRESPONDENCE 



THE DISCOVERY OF CACULUS 



To THE Editor of Science : Tlie writer de- 

 sires to call attention to certain disclosures 

 here pointed out for the first time, whose 

 conclusions are decisive in the matter of the 

 celebrated controversy between Newton and 

 Liebniz, regarding the discovery of calculus. 

 It is admitted that Leibniz was in full pos- 

 session of his calculus, at the time of his 

 second visit to London, in September, 167f>-, 

 and that during the week in London, he made 

 copious extracts from Newton's " De Analysi 

 jEquationes Numero Terminorum Infinitas," 

 which was in the hands of Collins, where it 

 had been placed by Barrow in 1669, with the 

 consent of Newton.^ Besides containing the 

 binomial theorem, expansions of trigonometric 

 functions, etc., it was a complete treatise on 

 fluxions. Found among Collins's papers after 

 his death, it was published in 1711. 



Leibniz's first information from Newton 

 that this work existed, and where it was to be 

 found, came from Newton's second letter of 

 October 26, 1676, which reached Leibniz some 

 months later in Germany. I quote the " En- 

 cyclopedia Britannica " (Inf. Calc.) as to the 

 contents of this letter: 



Newton proceeds to state that about 1669 he 

 eommunieated through Barrow to CoUiiis a com- 

 pendium of his method subsequently called "the 

 method of fluxions," with applications to areas, 

 rectification, cubature, etc. In this letter, how- 

 ever, he gave no explanation of this method, care- 

 fully concealing its nature in an anagram of 

 transposed letters. . . . 



Leibniz's reply to this letter has been termed 

 one of " noble frankness " in contrast to 

 Newton's secrecy. This frankness, however, 

 did not consist in infoiTaing Newton of the 

 week but recently spent with Collins, in care- 

 ful examination of the very compendium to 

 which he referred, and that his anagram was 

 useless. On the contrary, Leibniz renewed 

 statements of ig-norance of Newton's method, 

 and with seeming frankness, imparted his cal- 

 culus to Newton in every detail, thereby lay- 

 ing the foundation of a plot to deprive New- 

 1 Cajori, "A History of Mathematics," p. 230. 



ton of all credit, whose subsequent details 

 were carried out on a timed schedule. 



Thus, on the first publication of a work on 

 fluxions by Newton in 1704, an unsigned and 

 unfavorable review in the " Leipzig Acts " for 

 1705, stated that Newton uses and always has 

 used fluxions for the differences of Leibniz. 

 A few years later, Leibniz, who was the author 

 of this indirect charge, made it still clearer 

 in a letter to Count Bathmar, which was pub- 

 lished, stating that Bernouilli had written to 

 him that Newton had apparently fabricated 

 his calculus after having seen his own. Later 

 than this, again, a letter was distributed over 

 Europe, making the same direct charge, but 

 without containing the name of its author, 

 printer or place of publication. 



From Leibniz's examination of Newton's 

 compendium of fluxions on his second visit 

 to London, it is absolutely certain that he 

 possessed personal knowledge that these in- 

 famous charges against Newton were false. 



It must be explained how Leibniz knew of 

 the existence of that compendium in CoUins's 

 hands when he went to London, out of his way 

 from Paris to Hanover, and how he knew that 

 it contained what he wished to see. Newton's 

 fii'st letter to Leibniz, June 13, 1676, gave all 

 the important theorems on series which were 

 contained in that compendium, although his 

 letter neither stated this fact, nor gave ex- 

 planations. In his reply of August 27, 1676, 

 Leibniz expressed great interest, and asked for 

 their explanation and then shortly after went 

 to London and read all about them, the op- 

 portunity for this journey being a request 

 from the Duke of Hanover to return to Ger- 

 many. 



The only reasonable supposition is that 

 Leibniz had seen this manuscript on his first 

 visit to London, in 1673, and thus knowing of 

 its existence, and that it contained these series, 

 the new interest which they aroused caused 

 the second visit, for the purpose of re-reading 

 them in the light of an^ improved mathemat- 

 ical knowledge. 



The probability of the truth of this sup- 

 position is increased when we take into ac- 

 count the character of the man and the cir- 



