MATHEMATICAL FICTIONS. 267 



of relative motion of the matter constituting an individual atom ;" and 

 that ' ' he investigated the relation between their diameters, the num- 

 ber in a given space, and the mean length of path from impact to 

 impact, and so gave the foundation for estimates of the absolute 

 dimensions of atoms." Also that " Loschmidt, in Vienna, had 

 shown, and not much later Stoney, independently, in England, show- 

 ed how co reduce from Clausius and Maxwell's kinetic theory of gases 

 a superior limit to the number of atoms in a given measurable space." 



The confiding auditor follows the President through further dis- 

 quisitions on the " superlatively grand question, what is the inner 

 mechanism of an atom ?" and a minute and most definite description 

 of the "regular elastic vibrations" of "the ultimate atom of 

 sodium," of the manner in which " any atom of gas, when struck 

 and left to itself, vibrates with perfect purity its fundamental note or 

 notes," and how, " in a highly attenuated gas, each atom is very 

 rarely in collision with other atoms, and therefore is nearly at all 

 times in a state of true vibration," while " in denser gases each atom 

 is 'frequently in collision ;" besides a great deal more, in all of which 

 the existence of these atoms is coolly taken for granted, and treated 

 as a fundamental established scientific fact. 



After hearing all these oracular utterances concerning atoms, the 

 unsophisticated listener before mentioned will be surprised to learn 

 that no human being has ever seen an atom of any substance what- 

 ever ; that there exists absolutely no direct evidence of the existence 

 of any such atoms ; that all these atoms of which Sir W. Thomson 

 speaks so confidently and familiarly, and dogmatically, are pure fig- 

 ments of the imagination. 



He will be still further surprised to learn that the bare belief in 

 the existence of ultimate atoms as a merely hypothetical probability 

 is rejected by many of the most eminent of scientific men, and that 

 among those who have disputed the idea of the atomic constitution 

 of matter, is the great Faraday himself ; that the question of the 

 existence or non-existence of atoms has recently been rather keenly 

 discussed ; and that even on the question of the permissibility of ad- 

 mitting their hypothetical existence, scientific opinion is divided ; and 

 that such a confident assumption of their existence as forms the basis 

 of this part of the President's address is limited to only a small sec- 

 tion of mutually admiring transcendental mathematicians, Sir W. 

 Thomson being the most admired among them, as shown by the 

 address of Professor Tait to Section A. 



It would have been perfectly legitimate and most desirable that Sir 

 "W. Thomson should give the fullest and most favorable possible 

 statement of the particular hypotheses upon which he and his friends 

 have exercised their unquestionably great mathematical skill ; but he 

 should have stated them as what they are, and for what they are 

 worth, and have clearly distinguished between such hypotheses and 

 the established facts of universally admitted science. Instead of 

 doing this, he has so mixed up the actual discoveries of indisputable 

 facts with these mere mathematical fancies as to give them both the 

 semblance of equally authoritative scientific acceptance, and thus, 

 without any intention to deceive anybody, must have misled nearly 

 all the outside public who have heard or read his address. 



As these letters are mainly intended for those who are too much 

 engaged in other pursuits to study science systematically, and as 



