288 PETER GUTHRIE TAIT 



The first form of the equation gives 



so that the same force now appears as the space-rate at which kinetic energy changes ; 

 or, if we please, as the space-rate at which energy is produced by the force. 



Here are some of Mr Spencer's comments: "force is that which changes the 

 state of a body ; force is a rate, and a rate is a relation (as between time and distance, 

 interest and capital) ; therefore a relation changes the state of a body." 



The contradiction which Mr Spencer detects here, and over which he waxes 

 eloquent and defiant, exists in his own mind only. The anthropomorphism which 

 has misled him is but a convenient and harmless relic of the old erroneous interpreta- 

 tions of the impressions of sense. 



In his reply (Nature, Dec. 2, 1880) Herbert Spencer reproduced a good 

 deal of his pamphlet, got somewhat indignant over a side issue, and sneered 

 at Tail's mathematics. "If," he remarked, "his mathematics prove that 

 while force is an agent which does work, it is also the rate at which an 

 agent does work, then I say so much the worse for mathematics." In a 

 brief rejoinder (Nature, Dec. 9, 1880) Tait wrote: 



Mr Spencer has employed an old remark of Prof. Huxley as to what mathematics 

 can, and cannot, do ; but he has not employed it happily, for the question at issue is 

 really this : is it correct to speak, at one time, of force as an agent which changes 

 a body's state of rest or of motion, and again to speak of it as the time-rate at which 

 momentum changes or as the space-rate at which energy is transformed ? 



I answer that there is not the slightest inconvenience here ; except, perhaps, in the 

 eyes of those metaphysicians (if there be any) who fancy they know what force is. 

 Such phrases as "the wind blows" or "the sun rises" though used by the most 

 accurate even of scientific writers, would otherwise (on account of their anthropomorphism) 

 have to be regarded as absolute nonsense. 



Here the controversy ended, for Spencer's later letter of Dec. 16 took no 

 notice of the scientific questions which were supposed to be the subjects of a 

 discussion which he himself had originated. Tait regarded the controversy 

 as a joke ; for he knew it was hopeless to convince of any errancy a mind 

 which believed that the greatest physical generalization of modern times could 

 be established as an a priori intuition. 



