May 20, 1S80] 



NATURE 



independent of any consideration of motion. Force 'was 

 often defined to be that which caused or tended to cause 

 motion ; but the theory of the combination and resolution 

 of forces was founded on certain assumed axioms about 

 the properties of forces without further reference to the 

 effect by which force was described. The proof of the 

 parallelogram of forces was to most beginners such a 

 formidable pons asinorum that the broad conception 

 that velocities, accelerations, and forces acting at given 

 points were all fully represented by vectors, and that each 

 could be added just in the same way as the vectors which 

 represented them, was not soon grasped by the mind. 

 Consideration of the fundamental principles of dynamics 

 and of the philosophic position of the first law of motion, 

 which at the same time defines the measure of time and 

 states a law of nature, was avoided, and the theory of the 

 motion of matter became a development of the equations 

 of statics. 



Thomson and Tail returned to the order of Newton 

 and abolished artifices from the foundations of the science 

 of dynamics. The influence of Thomson and Tait's 

 "Natural Philosophy" on the volume before us is appa- 

 rent in the first chapter. The proofs of the parallelogram 

 of forces by Duchayla and Duhammel are conspicuously 

 absent, and the fundamental proposition of statics is 

 deduced quite naturally from consideration of the 

 parallelogram of velocities. When it is once admitted 

 that statics should rest on Newton's laws of motion, the 

 appropriateness of a separate treatise on the subject, to 

 include electrostatics and elasticity, becomes question- 

 able. Why should dynamics be divided and a separate 

 treatise be written on that portion from which it is 

 possible to exclude the idea of mass ? A book on the 

 analysis of systems of forces or " wrenches " deals with a 

 natural group of propositions, so does a book on attrac- 

 tions, on electrostatics, or the relations of stresses and 

 strains. But we cannot see that it is natural to group 

 those subjects together with the view, as it would appear 

 that the student should make himself acquainted with 

 them before mastering the dynamics of a particle. Indeed, 

 however we may admire each chapter of Prof. Minchin's 

 work, we cannot help regretting that he has limited his 

 subject-matter by the title of the volume. 



At the end of each chapter is an abundant selection of 

 examples— a very necessary part of an educational work 

 on any department of mathematics. It would have been 

 well that amongst these should have been found a larger 

 proportion of examples demanding a numerical answer ; 

 the best students show a liability to failure in rapidly 

 dealing with dynamical questions when concrete numbers 

 take the place of the more familiar symbols. 



It is not often that a graduate of Dublin University 

 omits to set forth in its proper place the work of a Dublin 

 professor. Any one would have looked with considerable 

 confidence in Chapter X. of Minchin's "Statics" for some 

 account of Ball's theory of screws as a sequel to Poinsot's 

 central axis, but he would be disappointed. As that 

 theory is very instructive as well as exceedingly elegant, 

 the omission is a loss to the student. 



Chapter IX. is devoted to friction, and ends with four 

 articles on the friction of a pivot, based on the assumption 

 that the pressure between pivot and footstep is uniform 

 over the surfaces in contact ; and in Art. 134 the equation 



of the tractory is found by a further condition that the 

 vertical wear shall be constant. As a fact, when a pivot 

 has been at work for some time the vertical wear becomes 

 of necessity constant, and thence may be deduced the 

 normal pressure at any point which will not be constant 

 unless the form of the pivot be the tractory. As an illus- 

 tration we propose the following to our readers : A conical 

 footstep is to bear a maximum load with a minimum 

 frictional moment ; show that it should have a hole in the 

 middle one-third the diameter of the footstep. A similar 

 consideration may be applied to ascertain the distribution 

 of pressure between a horizontal shaft and an ordinary 

 bearing. 



The book ends with a chapter on stresses and strains 

 and their relation to each other. The examples appended 

 to this chapter will be found most useful to the student ; 

 so far as we know he will not find elsewhere such facilities 

 for testing his skill in this department of dynamics. 

 Although we do not think it desirable that the depart- 

 ments of the science of dynamics should be classified for 

 teaching purposes into statics and kinetics so completely 

 as the present volume implies, we can heartily recommend 

 each several chapter for the subject on which it treats, and 

 we hope that Prof Minchin will produce a work dealing 

 with kinetics, and that when a fresh edition of both is 

 demanded he will weld them into a single treatise on 

 dynamics. 



AUSTRALIAN ORCHIDS 



Australian Orchids. By R. O. Fitzgerald, F.L.S. Part V. 



(Sydney, N.S.W.) 



THE part of this beautiful and instructive work which 

 has just reached us contains ten plates, illustrations 

 of si.xteen species belonging to the genera Prasophyllum, 

 Thelymitra, Sarcochilus, Dendrobium, Pterostylis, Cleiso- 

 stoma, and Bolbophyllum, all full of analyses, displaying 

 in a very satisfactory manner the forms, disposition, and, 

 in many instances, the development of the reproductive 

 organs ; whilst the letterpress is as full as is that of 

 previous parts, of curious and instructive observations on 

 the habits of the species and their modes of fertilisation. 

 Whether, in point of scientific importance, or fulness of 

 illustration, there are few works upon the Orchidere to 

 compare with this, certainly none at all comparable to it 

 has ever been attempted in a colony. Its only rivals are 

 the magnificent orchideous plates in Blume's " Rumphia," 

 and in his still more beautiful " Orchidea; of the Indian 

 Archipelago." On the other hand, in respect of descrip- 

 tive matter the works of these two authors widely differ. 

 Blume had to deal with a host of previously unanalysed 

 and unnamed generic and specific forms, which he classi- 

 fied and described in a truly inasterly manner, and his 

 works are hence almost purely systematic. The materials 

 for the "Australian Orchids" had been for the most part 

 classified by Brown in the "Prodromus Flora Novas 

 Hollandia:," with a skill equal to that subsequently dis- 

 played by Blume in respect of the Indian ones, and Mr. 

 Fitzgerald has therefore rightly devoted his descriptive 

 matter chiefly to the "life-history" of the species. As a 

 specimen of this we may quote his observations on 

 Prasophyllum Jimbriaium: — 



" This little flower presents another of the anomalies 



