MATHEMATICAL FICTIONS. 253 



and most definite description of the "regular elastic vibra- 

 tions" 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 whatever; that there exists absolutely 

 no direct evidence of the existence of any such atoms; that 

 all these atoms oi which Sir W. Thomson speaks so confi- 

 dently and familiarly, and dogmatically, are pure fragments 

 of the imagination. 



He will be still further surprised to learn that the bare 

 belief in the existence of ultimate atoms as a merely hypo- 

 thetical probability is rejected by many of the most emi- 

 nent 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 exist- 

 ence or non-existence of atoms has recently been rather 

 keenly discussed; and that even on the question of the per- 

 missibility of admitting their hypothetical existence, scien- 

 tific opinion is divided; and that such a confident assump- 

 tion of their existence as forms the basis of this part of the 

 President's address is limited to only a small section 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 desir- 

 able 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 unques- 

 tionably great mathematical skill; but he should have 

 stated them as what they are, and for what they are worth. 



