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III. On Newton's "Regula Tertia Philosophandi^ By the 

 Rev. Professor Challis, M.A., F.R.S., F.R.A.S.* 



THE Third Book of Newton's Rrincipia, to which exclu- 

 sively the title " De Mnndi Systemate " is attached, 

 contains at its beginning four Rules of Philosophizing, each 

 accompanied by explanations. Of these rules, the first, second, 

 and fourth, with their explanations, have been very generally 

 accepted, and do not require special consideration. The Third 

 Rule, which is enunciated in these terms, " The qualities of 

 bodies which admit neither of increment nor decrement, and 

 which pertain to all bodies on which experiments can be made, 

 are to be considered qualities of universal bodies," is accom- 

 panied by special explanatory remarks and definitions respect- 

 ing the ultimate qualities of bodies. The purpose of this com- 

 munication is to indicate the necessity of accepting this rule 

 in conducting physical theory, and to discuss the definitions 

 Newton has appended to it. 



The object I have in view requires commencing with the 

 premise that all theoretical research for explaining experi- 

 mental facts is carried on by means of calculation, which in 

 essence is reasoning conducted by symbols of quantity. The 

 application of reasoning by calculation for acquiring know- 

 ledge consists of three distinct processes : — (I.) Making hypo- 

 theses (i. e. foundations of calculation); (II.) deriving equa- 

 tions by means of the hypotheses from the data of proposed 

 questions; (III.) solving the equations, according to previously 

 ascertained rules, for obtaining the answers to the questions. 

 In order to establish the truth and necessity of this method of 

 theoretical inquiry, I shall bring under review the various 

 stages of its application, beginning with the earliest as re- 

 gards both the mathematics employed and the physical data. 

 As there will be occasion to revert repeatedly to the several 

 parts, I shall designate them respectively as parts (I.), (II.), 

 and (III.). 



It is well known that arithmetical calculation, such as that 

 now practised, had its origin in India, where " the device of 

 place/' according to which the value of a figure is determined 

 by its place relative to other figures in the same row, was 

 invented. This expedient, which appears to have been 

 unknown to the Greeks and Romans, and without which it 

 was hardly possible that much progress could be made in cal- 

 culation, was imported into Europe by the Arabians. Whether 

 or not they derived Algebra from the same quarter, it is cer- 

 tain that the Arabic name, which properly signifies the oppo- 



* Communicated by the Author. 



