234 Prof. J. G-. MacGregor on the 



uniform motion is unintelligible or meaningless, unless you 

 specify its direction and velocity with reference to a set of 

 axes," whereas the real objection is that the laws themselves, 

 in their usual form, are unintelligible, unless the axes are 

 specified, to which the uniform motion or acceleration men- 

 tioned in them is referred. His criticism is therefore neces- 

 sarily somewhat wide of the mark. It may be summarized 

 thus: — (1) Uniform motion is perfectly intelligible; and 

 therefore no specification of axes is necessary in the enun- 

 ciation of the first law. (2) The difficulties in the way of 

 specifying axes are practically insurmountable. 



With regard to (1), it will be noted that it rests entirely on 

 the intelligibility of uniform motion, and does not therefore 

 touch the necessity of the specification of axes in the case of 

 the second law * or of the first law in the form which Prof, 

 Lodge has given it himself: — "Without force there can be 

 no acceleration of matter "f. For in neither case is there 

 any reference to uniform motion. 



With regard to the intelligibility of uniform motion, while 

 it cannot be admitted that " such notions as axes of reference 

 are not at all necessary for the apprehension of what is meant 

 by a uniform velocity " (seeing that a uniform velocity is one 

 "whose magnitude and direction do not change relatively to 

 the axes employed in its specification), it is nevertheless 

 obvious that the specification of particular axes is not neces- 

 sary for this purpose. But the intelligibility of the first law 

 requires more than the mere apprehension of what is meant 

 by uniformity of velocity. For it is not a mere statement 

 about uniform velocity, but an assertion that a particle in 

 given circumstances must have a uniform velocity. Now a 

 velocity which is uniform with respect to one set of axes may 

 be variable with respect to others. It is therefore at once 

 obvious that, if we employ the ordinary conception of force, 

 the assertion which the law makes cannot hold for all axes, 

 and consequently can have no definite meaning, unless 



Leipzig, 1883), L. Lange (Ber. d. K. Sachs. Ges. d. Wiss. zn Leipzig, Math.- 

 phys. Classe, Bd. xxxvii. 1885, p. 338, and Die geschichtliche Entwicktlwng 

 des Bewegungsbegrifes, Leipzig, 1886), and Muirhead (Phil. Mag. [5] 

 vol. xxiii. 1887, p. 473), the last, however, being mentioned subsequently 

 in a footnote. 



* Mach, Streintz, Lange, and other German writers refer to the rela- 

 tivity of the first law merely, because they employ as second law Galileo's 

 law of the " physical independence of forces ' (Unabhangigkeitsprincip). 

 The second law to which I refer is Newton's second law. 



f ' Nature/ vol. xlviii. p. 62. 



