HYPOTHESES OP DYNAMICS. 21 



Finally, if the hypothesis that natural forces may be regarded as central forces be 

 adopted as an additional law of motion, these laws are found to be capable of considerable 

 condensation. For a.s the first law is but a particular case of the second, and as the third 

 law is included in the proposed fourth law, the first and third should not be enunciated 

 as distinct hypotheses. While, therefore, it may be advantageous for educational pur- 

 poses to break up the laws of motion into smaller or larger portions according to the 

 mental digestive power of the students under instruction, they may logically be enunciated 

 in two statements, which may be formulated somewhat as follows : — 



Tlie Lena of Force. — Relatively to any set of particles free from the action of force and 

 having the same velocity, the acceleration produced in another particle by a force is pro- 

 portional to the force and has the same direction. 



The Laiu of Stress. — Natural forces may be considered to be attractions or repu.lsions 

 whose magnitudes vary solely with the distances of the particles between which they 

 act. 



It may be objected to this condensing of the laws of motion into two statements that 

 different portions of these statements have received difierent degrees of verification, and 

 that we are thus more sure of some parts than we are of others. There is, however, no 

 means so far as I know of making a quantitative estimate of the amount of verification 

 which the different parts into which these statements might be broken up, have received ; 

 and it is thus impossible to divide them into portions whose parts have received the same 

 verification, except by dividing them into portions which would be themselves indivisible. 

 This of course might be done. But the relative amount of verification would seem to be 

 unimportant. The only requisite of our formulated axioms is that they should be axiom- 

 atic, that is, that they should really represent the fundamental hypotheses which, either 

 in the form in which they are enunciated or in some other form, are actually employed 

 in dynamical investigations. 



It will be noted that the law of stress is so formulated above, following Helmholtz, 

 as to be obviously temporary. Even the most strenuous supporter of contact action may 

 admit that though action at a distance is not to be admitted as a fact, dynamical pheno- 

 mena may be deduced from hypotheses expressed in terms of action at a distance as a 

 fiction. When dynamical science has made further advances, the above laws will, probably 

 have to give way to others more closely corresponding to the advanced state of the 

 science. Meantime, however, the law^s given above seem to me to represent better than 

 any others the present fundamental hypotheses of abstract dynamics. 



