498 



SCIENCE. 



[Vol. II., No. 30. 



j)ast and present, have placed him in the front 

 rank of the cultivators of that science. His 

 contributions to part ii. are duly accredited to 

 him in the above-mentioned schedule. 



The original object of this treatise is stated 

 to bq twofold ; viz., " to give a tolerabl}- com- 

 plete account of what is now known of natural 

 philosoph3', in language adapted to the non- 

 mathematical reader, and to furnish to those 

 who have the privilege which high mathematical 

 acquirements confer, a connected outline of 

 the analytical processes by which the greater 

 part of that knowledge has been extended into 

 regions as j'et unexplored hy experiment." 



From the nature of the case, the success of 

 the authors in the attainment of their first object 

 was small, compared with the second ; for in 

 order to give an intelligible account, to one un- 

 accustomed to mathematical reasoning, of the 

 general tenor and results of such reasoning, 

 requires not onlj' capacities such as few mathe- 

 maticians have had in our daj', except Clifford , 

 but requires, also, an amount of space incom- 

 patible with the second and principal object 

 which the authors had in view. In order, 

 however, better to reach the non-mathematical 

 reader, the authors published a work entitled 

 ' Elements of natural philosophj-, part i.,' 

 which was only an abridgment of 'this 'trea- 

 tise,' made by simply omitting all the advanced 

 mathematical developments. 



The second and principal object, however, 

 of the authors, was one in which thej^, perhaps, 

 were better fitted to succeed than auy who 

 could be selected. Their object was a large 

 one, and its attainment was undertaken in a 

 large way. It involved the presentation of the 

 general subject of kinematics, or the geometry 

 of motion considered apart from the forces 

 causing it, including the exposition and use of 

 generalized co-ordinates ; and the considera- 

 tion of harmonic motion, which " uaturallj^ 

 leads to Fourier's theorem, one of the most 

 important of all analytical results as regards 

 usefulness in physical science," and including, 

 also, the higher parts of the analj'tical discus- 

 sion of curves and surfaces in space, of three 

 dimensions. Next it required an extended 

 development of dynamical laws and principles 

 founded on Newton's Principia, comprising the 

 dynamics of a particle and of a rigid body, 

 and the whole of what is now termed kinetics 

 worked over and " developed from the grand 

 basis of the conservation of energy-." The 

 scope of the work demanded, also, the estab- 

 lishment of the principal formulae of spherical 

 harmonics, a branch of analysis whose charac- 

 ter we shall explain more at length hereafter. 



All these and other subjects, which are usu- 

 allj- regarded as but distantly related to the 

 subject in hand, form a necessary- part of a 

 work whose object is as wide as that proposed 

 by the authors. But it is hardly too much to 

 saj-, that every important thoorj- treated has 

 received at theii' hands, not only elucidation, 

 but additions of importance. 



In order to make this paper as useful as 

 maj' be, it has seemed best, in what follows, to 

 content ourselves with the attempt to give an 

 account to mathematical readers of the more 

 important developments contained in the work, 

 and not to engage in the task of trying to make 

 an elucidation of its contents suitable for the 

 general reader. 



When we come to consider in particular the 

 contents of part ii., it is found to be upon 

 the general subject of statics; though man}' 

 subjects, such as elasticity, the tides, etc., not 

 usuallj- treated in works on that subject, are 

 here included. It consists of three chapters, 

 the first of which is but five pages in length, 

 and is merely introductory. It states and illus- 

 trates the utter impossibility of submitting the 

 exact conditions of anj' phj^sical question to 

 mathematical investigation by reason of our 

 ignorance of the nature of matter and molecular 

 forces, but shows that approximate solutions 

 obtained bj- neglecting forces which do not af- 

 fect the conclusions sought to be established, 

 and bj' regarding bodies as rigid which are 

 iiearlj' so, lead to practicall}' the same results, 

 as to the equilibrium and motion of bodies, as 

 we should be led to bj' the solution of the infi- 

 nitely' more transcendent problem which has 

 regard to all the forces acting. 



In case, however, we consider the bending 

 or other deformations of bodies regarded as 

 elastic, we make a second approximation to 

 the exact treatment of physical questions ; and, 

 by introducing modifications of elasticity due 

 to changes of temperature, we should make a 

 third approximation, which might be cairied 

 one step fiirther bj' taking account of conduc- 

 tion of heat, and farther still by considering 

 the modifications of ordinarj' conduction due 

 to thermo-electric currents, etc. In view of all 

 this, the authors saj', " The object of the pres- 

 ent division of this volume (i.e., part ii.) is 

 to deal with the first and second of these ap- 

 proxiinations. In it we shall suppose all solids 

 either rigid (i.e., unchangeable in form and 

 volume) or elastic; but, in the latter case, we 

 shall assume the law connecting a compression 

 or a distortion with the force which causes it, 

 to have a particular form deduced from ex- 

 periment. . . . We shall also suppose fluids, 



