July 6, 1876] 



NATURE 



207 



priate training for his subsequent labours in the survey of 

 the sciences in their widest extent. 



" It has always appeared to me," says Mr. Todhunter, 

 " that Mr. Whewell would have been of great benefit to 

 students if he had undertaken a critical revision of the 

 technical language of Mechanics. This language was 

 formed to a great extent by the early writers at an epoch 

 when the subject was imperfectly understood, and many 

 terms were used without well-defined meanings. Gradu- 

 ally the language has been improved, but it is still open 

 to objection." 



In after years, when his authority in scientifi:. termi- 

 nology was widely recognised, we find Faraday, Lyell, 

 and others applying to him for appropriate expressions 

 for the subject-matter of their discoveries, and receiving 

 in reply systems of scientific terms which have not only 

 held their place in technical treatises, but are gradually 

 becoming familiar to the ordinary reader. 



" Is it not true," Dr. Whewell asks in his Address to the 

 Geological Society, "in our science as in all others, that a 

 technical phraseology is real wealth, because it puts in 

 our hands a vast treasure of foregone generalisations.'"' 



Perhaps, however, he felt it less difficult to induce 

 scientific men to adopt a new term for a new idea than to 

 persuade the students and teachers of a University to alter 

 the phraseology of a time-honoured study. 



But even in the elementary treatment of Dynamics, if 

 we compare the text-books of different dates, we cannot 

 fail to recognise a marked progress. Those by Dr. 

 Whewell were far in advance of any former text-books as 

 regards logical coherence and scientific accuracy, and if 

 many of those which have been published since have fallen 

 behind in these respects, most of them have introduced 

 some slight improvement in terminology which has not 

 been allowed to be lost. 



Dr. Whe well's opinion with respect to the evidence of 

 the fundamental doctrines of mechanics is repeatedly 

 inculcated in his writings. He considered that experi- 

 ment was necessary in order to suggest these truths to 

 the mind, but that the doctrine when once fairly set 

 before the mind is apprehended by it as strictly true, the 

 accuracy of the doctrine being in no way dependent on 

 the accuracy of observation of the result of the experi- 

 ment. 



He therefore regarded experiments onthe laws of motion 

 as illustrative experiments, meant to make us familiar 

 with the general aspect of certain phenomena, and not as 

 experiments of research from which the results are to be 

 deduced by careful measurement and calculation. 



Thus experiments on the fall of bodies may be re- 

 garded as experiments of research into the laws of gravity. 

 We find by careful measurements of times and distances 

 that the intensity of the force of gravity is the same what- 

 ever be the motion of the body on which it acts. We 

 also ascertain the direction and magnitude of this force on 

 different bodies and in different places. All this can only be 

 done by careful measurement, and the results are affected 

 by aU the errors of observation to which we are liable. 



The same experiments may be also taken as illustra- 

 tions of the laws of motion. The performance of the 

 experiments tends to make us familiar with these laws, 

 and to impress them on our minds. But the laws of 

 motion cannot be proved to be accurate by a comparison 



of the observations which we make, for it is only by taking 

 the laws for granted that we have any basis for our calcu- 

 lations. We may ascertain, no doubt, by experiment, 

 that the acceleration of a body acted on by gravity is the 

 same whatever be the motion of that body, but this does 

 not prove that a constant force produces a constant ac- 

 celeration, but only that gravity is a force, the intensity 

 of which does not depend on the velocity of the body on 

 which it acts. 



The truth of Dr. Whewell's principle is curiously illus- 

 trated by a case in which he persistently contradicted it. 

 In a paper communicated to the Philosophical Society ot 

 Cambridge, and reprinted at the end of his " Philosophy of 

 the Inductive Sciences," Dr. Whewell conceived that he 

 had proved, a pt tori, that all matter must be heavy. He 

 was well acquainted with the history of the establishment 

 of the law of gravitation, and knew that it was only by 

 careful experiments and observations that Newton ascer- 

 tained that the effect of gravitation on two equal masses 

 is the same whatever be the chemical nature of the bodies, 

 but in spite of this he maintained that it is contrary 

 not only to observation but to reason, that any body 

 should be repelled instead of attracted by another, where- 

 as it is a matter of daily experience, that any two bodies 

 when they are brought near enough, repel each other. 



The fact seems to be that, finding the word weight 

 employed in ordinary language to denote the quantity ot 

 matter in a body, though in scientific language it denotes 

 the tendency of that body to move downwards, and at 

 the same time supposing that the word mass in its scien- 

 tific sense was not yet sufficiently established to be used 

 without danger in ordinary language, Dr. Whewell en- 

 deavoured to make the word weight carry the meaning 

 of the word mass. Thus he tells us that " the weight of 

 the whole compound must be equal to the weights of the 

 separate elements." 



On this Mr. Todhunter very properly observes : — 



"Of course there is no practical uncertainty as to this 

 principle ; but Dr. WheweU seems to allow his readers to 

 imagine that it is of the same nature as the axiom that 

 ' two straight lines cannot inclose a space.' There is, 

 however, a wide difference between them, depending on 

 a fact which Dr. Whewell has himself recognised in 

 another place (see vol. i., p. 224). The truth is, that 

 strictly speaking the weight of the whole compound is 

 not equal to the weight of the separate elements ; for the 

 weight depends upon the position of the compound par- 

 ticles, and in general by altering the position of the 

 particles, the resultant effect which we call weight is 

 altered, though it may be to an inappreciable extent." 



It is evident that what Dr. Whewell should have said 

 was : " The mass of the whole compound must be equal 

 to the sum of the masses of the separate elements." This 

 statement all would admit to be strictly true, and yet not 

 a single experiment has ever been made in order to verify 

 it. All chemical measurements are made by comparing 

 the weights of bodies, and not by comparing the forces 

 required to produce given changes of motion in the 

 bodies ; and as we have just been reminded by Mr. 

 Todhunter, the method of comparing quantities of matter 

 by weighing them is not strictly correct. 



Thus, then, we are led by experiments which are not 

 only liable to error, but which are to a certain extent 

 erroneous in principle, to a statement which is universally 



