Nov. 15, 1883] 



NATURE 



agent, the full significance of which, when interpreted by 

 the light of modern discoveries, was first made clear by 

 Professors Thomson and Tait. An examination of New- 

 ton's original statement shows that in his view " equili- 

 brium is not a balancing of forces, but a balancing of the 

 effects of forces. When a mass rests on a table, gravity 

 produces in it a vertically downward velocity which is 

 continually neutralised by the equal upward velocity pro- 

 duced by the reaction of the table, and these forces . . 

 are equal because they produce in equal times equal and 

 opposite quantities of motion." 



As regards our knowledge of force as distinguished 

 from its mechanical measure as change of momentum, 

 we are reminded that our idea of force, originally de- 

 rived from the muscular sense, "may be a mere suggestion 

 of sense corresponding (no doubt) to some process going 

 on outside us, but quite as ditt'erent from the sensation 

 which suggests it, as is a periodic shearing of the ether 

 from brightness, or a periodic change of density of air 

 from noise." 



In discussing still further the nature of force, Prof 

 Tait points out that our belief in matter, the most certain 

 of all objective realities, is largely based on the property 

 of the unchangeability of its aggregate amount. " The only 

 other thing in the universe which is conserved as matter 

 is conserved is energy. Hence we conclude that energy 

 is the true physical reality, and force, which is merely the 

 space-rate at which energy is transformed, must be re- 

 garded like other expressions, such as rate of interest, 

 death-rate, gradient of heat, as an expression introduced 

 for convenience, and not necessarily because of an objec- 

 tive reality attached to it." 



Remembering the dual nature of all force as being 

 exerted between two bodies, we have, as another reading 

 of the Third Law, " Every action between two bodies is a 

 stress." 



With regard to potential energy, which must depend in 

 some hitherto unexplained way, like kinetic energy, on 

 motion. Prof. Tait says : " The conclusion which appears 

 inevitable is that, whatever matter may be, the other 

 physical reality in the universe which is never found 

 unassociated with matter, depends, in all its widely 

 varied forms, upon motion of matter." 



After explaining Newton's Laws, the author deals with 

 the principles of kinematics, and then with statics and 

 kinematics of various material systems, with different 

 degrees of freedom, inserting amongst the analytical 

 proofs several of those elegant geometrical constructions 

 for which he is so well known. Whilst the nature of the 

 article precludes a thorough exposition of the higher and 

 more involved parts of the subject, he has succeeded in 

 presenting illustrative problems of all the great divisions 

 in mechanics, which afford some insight into the nature 

 of the special parts of the subject to which they refer. 



Tnis most useful article, which exhibits the state of 

 knowledge in theoretical mechanics at the present time, 

 concludes with a list of the principal works on me- 

 chanics. 



Following Prof Tait's article, and under the heading of 

 "Applied Mechanics," we have the reprint of an article by 

 the late Prof Rankine, contributed by him to the volume 

 of the "Encyclopaedia Britannica" which was published 

 in 1857. 



In this article Prof. Rankine has dealt with the prin- 

 ciples of the subject very much on the same lines as in 

 his larger published work on "Applied Mechanics." It 

 is needless to say that nothing that Rankine wrote on the 

 theory of mechanics can ever become antiquated or 

 obsolete. He possessed such a firm grasp of the founda- 

 tions of the subject, that it seems impossible to believe 

 that on these points he could commit an error. But 

 since that time many new discoveries have been made in 

 mechanics, as in other sciences, to which we find no 

 reference in the present articles. Of these perhaps the 

 most important are the later developments of graphical 

 statics, and the kinematical analysis of Prof. Reuleaux. 

 The former subject, which really dates its origin from the 

 time of the discoveries by Rankine of the Theory of the 

 Extension of the Funicular Polygon, and by Clerk Maxwell 

 of the Theory of Reciprocal Figures, has received at the 

 hands of Culmann and others developments which are 

 now proving themselves of the greatest importance in 

 engineering design. Of the higher parts of these more 

 modern methods no information is given, either in the 

 article before us, or in the extremely clear and simple 

 theory of Frames, which appears in Prof. Jenkin's 

 article on " Bridges,'' in the fourth volume of this " Ency- 

 clopaedia," or in any other place in the work, and 

 having regard to the importance of the subject, we cannot 

 but regret its absence. 



We believe that had the work of Reuleaux been pub- 

 lished earlier, Rankine would have been one of the first 

 to recognise its beauty and value. 



The whole article displays the power of logical arrange- 

 ment and method, as well as the condensed style which 

 is so characteristic of all Rankine's writings, and makes 

 them such difficult reading for beginners. These will 

 probably prefer his " Applied Mechanics," for purposes of 

 study, to the article before us. But as .an exposition, in 

 small compass, of the leading principles of that science, it 

 is altogether admirable as far as it goes, whilst its value is 

 increased by the numerous articles in this " Encyclopaedia" 

 on special, more technical parts of the subject, such as 

 that of Prof Jenkin, already quoted, and that of Prof- 

 Unwin on " Hydraulics," and others which are promised 

 in forthcoming volumes. 



The article on " Mammalia," by Prof Flower, is an ex- 

 tremely well condensed and intelligibly written essay on 

 the highest class of vertebrate beings, for which, as the 

 author notes, there has never been a generally accepted 

 vernacular designation. Still the class known to zoolo- 

 gists as Mammals is one rigidly defined, and one that 

 obeys the strictest rules of logic in its definition, despite 

 Kant's remarks on the impossibility of defining strictly 

 natural objects. It is easy to imagine the mammary 

 glands reduced to a stateof extreme simplicity, but among 

 living mammals this never occurs, nor is there any gland 

 to be confounded with them in any other vertebrate form. 

 The article opens with a chapter on the general anatomi- 

 cal characters of the class, in which an immense amount 

 of accurate information is compressed into a small space. 

 Many of the figures illustrating the details of the osteology 

 are taken from Prof. Flower's well-known work on this 

 subject. In the chapter on classification, the recent argu- 

 ments of Prof. Huxley in favour of passing over all known 



