"NEWTON'S LAWS OF MOTION" 233 



foundations of dynamics. A small book of fifty-two pages, and entitled 

 Newton s Laws of Motion, was finally published in 1899 by A. and C. Black. 

 The book contained a brief introduction on Matter and Energy and then 

 two chapters on Kinematics and Dynamics respectively. In a review by 

 A. E. H. L. in the columns of Nature (Vol. LXI, January 18, 1900) the book 

 was commended as being 



"for the most part excellent, the geometrical methods employed being especially 

 elegant. Room is found for an elementary discussion of strain, of compounded simple 

 harmonic motions, of attractions, including the distribution of electricity on a sphere 

 under influence, and of the velocity of waves along a stretched cord, in addition to 

 interesting and unhackneyed accounts of the matters which are the stock in trade of 

 books on the elements of mechanics. The book on the whole is thoughtful, in many 

 parts it is much better than the current text-books on the subject, and the parts that 

 call for criticism are no worse than the corresponding parts of most other books on the 

 subject; but they are the most important parts, and they might have been so much 

 better. There was a great opportunity, but it has been missed." 



Part of the criticism virtually amounted to a complaint that certain sections 

 were not sufficiently expanded. Tail's own preface may be regarded as an 

 answer to this kind of objection ; for the book is explicitly stated not "to be 

 a text-book " but " a short and pointed summary of the more important 

 features of ... the basis of the subject." For example "to explain" (as was 

 desired by the critic) " the mathematical notion of a limit " requires not 

 " some space " but a good deal of space, if the explanation is to be complete. 

 Nevertheless, the following brief paragraphs show that the conception of 

 physical and dynamical continuity, on which fundamentally the notion of 

 the limit rests, was explicitly recognised by Tait : 



10. When we pass from the consideration of displacement to that of motion, 

 the idea of time necessarily comes in. For motion essentially consists in continued 

 displacement. In the kinematics of a point, all sorts of motion are conceivable : but 

 we limit ourselves to such as are possible in the case of A f article of matter. 



11. These limitations are simple, but very important. 



(a) The path of a material particle must be a continuous line. [A gap in it 

 would imply that a particle could be annihilated at one place and reproduced at 

 another.] 



(y9) There can be no instantaneous finite change in the direction, or in the 

 speed, of the motion. \Inertia prevents these, unless we introduce the idea of finite 

 transformations of energy for infinitely small displacements, or (in the Newtonian 

 system) infinite forces.].... 



14. If the speed be variable its value, during any period, must sometimes exceed 

 T. 3 



