NA TURK 



49 



THURSDAY, NOVEMBER 15, 1894. 



HISTORICAL EXPOSITION OF MECHANICS. 

 The Science of Mechanics: a Critical and Historical 

 Exposition of its Principles. By Dr. Ernst Mach, 

 Professor of Physics in the University of Prague. 

 Translated from the second German edition by Thomas 

 J. McCormack. (Chicago : The Open Court Publish- 

 ing Co. London : Watts and Co., 1893.) 

 nnHE appearance of a translation into English of this 

 J- remarkable book should serve to revivify in this 

 country the somewhat stagnating treatment of its sub- 

 ject, and should call up the thoughts which puzzle us 

 when we think of them, and that is not sufficiently often. 

 Prof. Mach isa striking instance of the combination 

 of great mathematical knowledge with experimental skill, 

 as exemplified not only by the elegant illustrations of 

 mechanical principles which abiunl in this treatise, but 

 also from his brilliant experiments on the photography 

 of bullets, which have been recently elaborated and 

 simplified by Mr. C. V. Boys. 



The appearance of the first edition, in 1883, is stated, 



I in the preface of the second edition, to have stimulated 



I the production of treatises by WohUvill, Streintz, Lang e, 



Epstein, MiiUer, Popper, Helm, Planck, Poske, and 



others, discussing theories of cognition in connection 



with Mechanics ; but it is curious that Maxwell's little 



tract on "Matter and Motion," of 1879, a veritable 



I master-piece on this subject, should appear to be unknown 



to the author, although mentioned in the translator's 



1 foot-notes. 



j The present volume is not a treatise upon the applica- 

 I tion of the principles of mechanics, to quote from the 

 preface. Its aim is to clear up ideas, expose the real 

 significance of the matter, and get rid of metaphysical 

 obscurities. Mechanics is treated not as a branch of 

 mathematics, but as one of the physical sciences ; and 

 the reader's interest is invited to know how the prin- 

 ciples of mechanics have been ascertained, from what 

 t sources they take their origin, and to what extent they 

 may be regarded as permanent acquisitions. All this, 

 the positive and physical essence of mechanics, which 

 i makes its chief and high interest for a student of nature, 

 I is in existing treatises completely buried and concealed 

 j beneath a mass of technical considerations. 



The gist and kernel of mechanical ideas has in almost 



! every case grown up in the investigation of very simple 



I and special cases of mechanical processes ; and the 



I analysis of the history of the discussions concerning these 



cases must ever remain the method at once the most 



effective and the most natural for laying this gist and 



kernel bare. Indeed, it is not too much to say that it is 



< the only way in which a real comprehension of the general 



I upshot of mechanics is to be attained. 



Acting upon the plan laid down in the citations above, 



i the author treats his subject from the historical order of 



; development, and begins with an Introduction of general 



remarks, illustrated by an Egyptian representation of 



the mechanical arts, and by a quotation from Vitruvius. 



Chapter i., on the Development of the Principles of 

 Statics and Hydrostatics, follows closely the historical 

 NO. 1307, VOL. 51] 



subject-matter given by Lagrange in the first section of 

 his " Mc'canique analytique"; but Prof. Mach's treat- 

 ment has the very great superiority of being profusely 

 illustrated by elegant diagrams, while Lagrange made a 

 point of banishing figures entirely from the " .Mccanique 

 analytique." 



Lagrange thus appears as a supporter of the ancient 

 tradition that Rational and Practical Mechanics were to 

 be considered as in a measure opposed to each other, 

 as Newton observes in his preface of the " Principia " ; 

 the latter being -an inferior branch of study, to be culti- 

 vated only for the sake of gain or some other material 

 advantage. 



To quote from Rankine's Preliminary Dissertation, 

 prefixed to his " Applied Mechanics '' : — 



"Archytas of Tarentuni might illustrate the truths of 

 Geometry by mechanical contrivances ; his methods were 

 regarded by his pupil Plato as a lowering of the dignity 

 of science. Archimedes, to the character of the first 

 geometer and arithmetician of his day, might add that of 

 the first mechanician and physicist — he might, by his 

 unaided strength acting through suitable machinery, 

 move a loaded ship on dry land — he might contrive and 

 execute deadly engines of war, of which even the Roman 

 soldiers stood in dread — he might, with an art afterwards 

 regarded as fabulous till it was revived by Buffon, burn 

 fleets with the concentrated sunbeams ; but that mechan- 

 ical knowledge and that practical skill, which in our eyes 

 render that great man so illustrious, were by men of 

 learning, his contempor.iries and successors, regaried 

 as accomplishments of an inferior order, to which the 

 philosopher, from the height of geometrical abstraction, 

 condescended with a view to the service of the State." 



We have only to study the progress of the essentially 

 modern science of Electricity to recognise the eloquent 

 truth of Rankine's words, in inveighing against the medi- 

 asval and ancient fallacy that there is a double system of 

 natural liizvs, one theoretical, geometrical, rational, dis- 

 coverable by contemplation, applicable to celestial, 

 a;therial, indestructible bodies, and being an object of 

 the noble and liberal arts ; the other practical, mechanical, 

 empirical, discoverable by experience, applicable to 

 terrestrial, gross, destructible bodies, and being an object 

 of what were once called the vulgar and sordid arts. 



Possessed with these prejudices, the scholar of ancient 

 and mediaeval times, and even of the present day, was 

 occupied in developing and magnifying the numerous 

 errors, and in perverting and obscuring the much more 

 numerous truths which are to be found in the writings of 

 Aristotle ; so that it is not surprising that the notion 

 arose of scientific men being unfit for the business of 

 life, and that various facetious anecdotes were contrived 

 illustrative of this notion, anecdotes which have been 

 handed down from age to age, and applied with little 

 variation to the eminent philosophers of every time. 



Returning to chapter i. of Prof. Mach's treatise, we 

 find that the Principle of the Lever, employed in the 

 writings of Archimedes, is the real foundation of the 

 Science of Statics, and not the Parallelogram of Forces, 

 as is generally taught ; this theorem, although sketched 

 out by Stevinus of Bruges, was first fully enunciated by 

 Varignon and Newton, about 16S7. In fact, the modern 

 treatment of Statics is almost entirely due to Varignon. 



Prof. Mach examines with the acumen of a meta- 



D 



