192 PETER GUTHRIE TAIT 



demonstrations were first given. From 331 to 336 of the first edition 1 

 these hydrokinetic problems are brought into touch with physical questions 

 of far-reaching import. The discussion concludes with the remark that 

 " it must be remembered that the real circumstances differ greatly, because 

 of fluid friction, from those of the abstract problem, of which we take leave 

 for the present." At a much later date Kelvin published a few papers on 

 closely connected problems. In these as in other papers, as well as in the 

 Treatise, constant use is made of Thomson's general theorem of " Laziness " 

 as Tait called it (see above p. 182). 



Chapters in and iv of Division i, on Experience and on Measures 

 and Instruments respectively, are brief, touching only on the more 

 fundamental aspects of the subject. 



Division n (Abstract Dynamics) opens with a short introductory chapter 

 of a few pages, followed by Chapter vi on Statics of a Particle. The 

 academic problem familiar to all students of statics is quite ignored. Four 

 short paragraphs give the solution of the general problem of a particle 

 in equilibrium, under the action of given forces, some of which may be 

 forces of constraint ; and the remaining part of the chapter is occupied 

 with the theory of attractions according to the Newtonian Law of the 

 inverse square. By the easy steps of Kelvin's geometrical extensions of 

 Newton's original demonstrations of the attraction of a spherical shell, the 

 reader is led by simple physical reasoning, with the minimum of mathematics, 

 to the enunciation and proof of Green's problem of the unique surface 

 distribution of matter satisfying the assigned potential values at the surface. 

 Attractions of ellipsoids and centrobaric bodies generally are discussed in 

 considerable detail ; and this leads to the simpler applications of spherical 

 harmonics to problems of attraction. It may be mentioned in passing 

 that some of the demonstrations are simplified in the second edition. 



Chapter vn is devoted to the equilibrium of solids and fluids, flexible 

 cords being included as constituting a kind of intermediate case between 

 the equilibrium of perfectly rigid solids and the deformation of perfectly 

 elastic solids. The transition from the flexible cord to the elastic wire 

 may seem at first sight abrupt, but it is not really so when regard is had 

 to the fundamental kinematical considerations involved. The whole mode 



1 These correspond to 320-325 of the second edition, the sections on Action which 

 originally preceded the hydrokinetic applications having been placed after them in the new 

 edition. 



