PROCEEDINGS OP PBOVINCIAL SOCIETIES. 303 



In identifying the mathematical natural philosophy of the Sur- 

 geons and Apothecaries with that alluded to by Lord Bacon, the 

 lecturer conceived that he should be best explaining the former, by 

 interpreting the character of the latter from legitimate authorities. 

 He therefore adduced quotations from that profound mathematician, 

 Roger Cotes, in illustration of the different classes of philosophers : 



** Qui physicam tractandam susceperunt," says Cotes, *' ad tres 

 fere classes revocari possunt." 



He mentions, as those of one class, the sticklers for occult quali- 

 ties and the school doctrines of Aristotle and the Peripatetics : but 

 as it was conceived that there was little danger, in modern days, of 

 philosophy resuming that character, all further notice of such 

 would be dismissed in Coles's own words : — " Cumque toti sint in 

 rerum nominibus, non in ipsis rebus ; sermonem quendam philosoi- 

 phicum censendi sunt adinvenisse, philosophiam tradidisse non sunt 

 censendi." 



Speaking of a second class he says, " Qui speculationum suarum 

 fundamentum desumunt ab hypothesibus ; etiarasi deinde secundum 

 leges mechanicas accuratissime procedant ; fahulam quidem elegan- 

 tera forte et ven\isi'd.m,fabulam tamen concinnare dicendi sunt." 



He next proceeds to describe the third class — that of true natural 

 philosophers : " Relinquitur ades tertium genus, qui philosophiam 

 scilicet experimental m profitentur. Hi quidem ex simplicissimis 

 quibus possunt principiis rerum omnium causas derivandas esse vo- 

 lunt : nihil autem principii loco assumunt, quod nondum ex phaeno- 

 menis comprobatum fuerit. Hypotheses non comminiscuntur, neque 

 in physicam recipiunt, nisi ut quaestiones de quarum veritate dispu- 

 tetur. Duplici itaque methodo incedunt, analytica et synthetica. 

 Naturae vires legesque virium simpliciores ex selectis quibusdam 

 phaenomenis per analysin deducunt, ex quibus deinde per synthesin 

 reliquorum constitutionem tradunt." 



According to this account, given by Cotes, we may affirm of 

 true natural philosophy — the " philosophia naturalis vera," of Lord 

 Bacon — the following propositions : 



L It is, in some degree, experimental; inasmuch as it assumes 

 nothing: as a principle which is not proved by observed phenomena. 



2. It either excludes hypotheses altogether, or only admits; 

 • them as questions of probability. 



3. It endeavours to derive the causes of all things from the 

 simplest possible principles. 



4. The methods of conducting its researches are two—the ansb. 

 lytical and the synthetical. 



Each of these propositions was then illustrated in turn. As 

 examples gf the first, it was shewn, hovy in the sciences of Optics 

 and Electricity a few experiments were taken as a foundation ; and 

 by assuming the facts which they established as principles, that these 

 sciences were gradually evolved by the means of mathematical rea- 

 soning, — " ope et interventu mathematicae." 



With respect to the second of these propositions, considerable 



