234 PETER GUTHRIE TAIT 



and sometimes fall short of the average value. But (by 1 1 (/9), above, and therefore 

 solely in consequence of inertia) the shorter the period considered, the more closely 

 will the actual speed of a material particle agree with the average value : and that 

 without limit. 



Again, very early in the book, Tait warned the reader against the 

 inevitable anthropomorphism which clings to our words and phrases ; yet 

 he was attacked for using Newton's anthropomorphic definition of force as 

 a cause and at the same time pointing out its true nature as simply a rate 

 of change of a quantity in time. As regards the general criticism that 

 Tait followed too slavishly Newton's presentation of the foundations of 

 dynamics, there is a great deal to be said on both sides. Tail's experience 

 had convinced him that for junior men Newton's method was the best, 

 dealing as it did with immediate sensations and perceptions. For that reason 

 he called the book Newton s Laws of Motion, 



But, although in this small pamphlet Tait felt himself compelled to adhere 

 to Newton's method, every one interested in the subject knew that he had in 

 one published paper attempted to establish the laws of motion on a wider 

 basis free from the explicit use of the word Force. This paper " On the 

 Laws of Motion, Part I," was printed (but only in Abstract) in the Proceedings 

 of the Royal Society of Edinburgh, 1882 ; and a German translation appeared 

 in a German mathematical journal. The Second Part was never written 

 out in a form suitable for publication. When busy with the preparation of the 

 1882 paper, Tait wrote to Cayley on Nov. 20, 1882, in these words : 



Do you know of any attempt to construct the whole system of Mechanics (for it 

 would, under the circumstances, be absurd to call it Dynamics') from general principles, 

 such as Conservation and Transformation of Energy, Least Action, etc., without intro- 

 ducing either Force, Momentum or Impulse? I have worked out a scheme of the kind 

 having been led to it by writing a long article for the Encyc. Brit. Not that it goes in 

 there, of course, but because in speaking of the anthropomorphic terms in which 

 Newton's Laws are expressed (e.g., a body compelled by force to do so and so ; a body 

 persevering in its state of etc. etc.) I tried to find out some simple mode of getting rid 

 of what I find Maxwell has called Personation. 



Of course, Force constantly comes in, but not in any sense as an agent, merely as 

 the space-rate of transformation of energy. It plays a part in some sense akin to that 

 of temperature-gradient in heat-conduction. But I see, by the words I have doubly 

 underlined, how very difficult it is to avoid anthropomorphism. I suppose it must 

 always be so, unless scientific men protest effectively against " the sun rises," " the wind 

 blows," etc. etc. 



If any such scheme has appeared, I should like to consider it before bringing my 

 notions before the R.S.E. 



