i 9 4 PETER GUTHRIE TAIT 



Mdcanique Analytique, is the prominence given to motion rather than to 

 equilibrium. Dynamical Laws and Principles are regarded as Preliminary ; 

 and then, as the first part of Abstract Dynamics, we are introduced to Statics 

 of particles, of solids, and of fluids. In a letter of 1863 (quoted above, page 

 181) Tail protested against Attractions being brought in before Properties 

 of Matter, of which they formed a natural part. It had become customary 

 and the custom still persists to treat Attractions and the theory of the 

 Potential as part of Statics of Particles. And yet, physically, attraction 

 means motion ; and equilibrium is maintained only by the introduction of 

 balancing forces of another type, cohesion, adhesion, surface constraint, etc. 

 Tail's suggestion to treat Gravitation as a property of matter was certainly 

 more in line with a truly logical arrangement than was the plan ultimately 

 adopted. But Thomson had already published a series of beautiful geo- 

 metrical demonstrations on the subject ; and no doubt he saw a splendid 

 chance of utilising this material and of working out far-reaching problems 

 of terrestrial dynamics. In other words, the problem of the earth's rigidity 

 dominated to a marked degree the composition of the whole section of 

 Abstract Dynamics which constituted Division n. Only in this way can 

 we explain the unusual scope of Chapter vn. No doubt Lagrange, in his 

 classical work, had included under Statics general discussions of the equi- 

 librium of flexible elastic wires and thin plates ; but Thomson and Tail 

 were the first to bring within the limits of one chapter the laws of equi- 

 librium of perfect fluids at rest or in steady rotation, and of solids ideally 

 rigid or deformable. Much of this chapter indeed belongs as truly to the 

 prospective section on the Properties of Matter as to the more abstract 

 branch of dynamics. Profound though the influence of " Thomson and Tait " 

 has been on the teaching and coordination of the principles of Natural 

 Philosophy, no later writers have followed their example in devoting a single 

 chapter to ordinary Statics of extended bodies, strings, and flexible wires, 

 to Hydrostatics, and to Elasticity. 



As regards the division of labour in the production of the book, I think 

 there are strong indications that there is more of Tail's initial work in the 

 earlier lhan in ihe laler portions of ihe volume, and lhal Thomson's hand is 

 particularly in evidence in the last chapter. Each was the other's severe 

 critic, and many a senlence must have undergone great internal changes under 

 ihe chiselling pen of each in lurn. 



It would be easy lo find, especially in ihe more elemeniary parts, some 



