NATURE 



169 



THURSDAY, JUNE 23, i{ 



THEORETICAL MECHANICS. 

 Theoretical Mechanics : an introductory treatise on the 

 Principles of Dynamics., with applications and numerous 

 examples. By A. E. H. Love, M.A., F.R.S., Fellow 

 and lecturer of St. John's College, Cambridge. Pp. 

 xiv + 379. (Cambridge : at the University Press, 

 1897.) 



THIS book is vibrating with dynamical modernity, 

 and proves in effect that Theoretical Dynamics 

 has not yet been reduced to the level of one of the 

 Exact Sciences ; and so it shows little tendency to 

 bridging over the gap still existing between the two 

 modes of treatment of the one science of Mechanics- 

 The two different methods are described by Newton in 

 the preface of the " Principia " — 



"Auctoris praefatio ad lectorem. Cum Veteres Me- 

 chanicam (uti Auctor est Pappus) in rerum Naturalium 

 investigatione maximi fecurunt ; et Recentiores, missis 

 formis substantialibus et qualitatibus occultis, Phaenomena 

 Nature ad leges Mathematicas revocare aggressi sint : 

 Visum est in hoc Tractatu Mathesin excolere, quatenus 

 ea ad Philosophiam spectat. 



" Mechanicam vero duplicem Veteres constituerunt : 

 Rationalem qute per Demonstrationes accurate procedit, 

 et Practicam. Ad Practicam spectant Artes omnes 

 Manuales, a quibus utique Mechanica nomen mutuata 

 est. Cum autem Artifices parum accurate operari solent, 

 sit ut Mechanica omnis a Geometria ita distinguatur, 

 ut quicquid accuratum sit ad Geometriam referatur, 

 quicquid minus accuratum ad Mechanicam. Attamen 

 errores non sunt Artis sed Artificum. . . . 



" Pars haec MechaniciE a Veteribus in Potentiis quin- 



que ad artes manuales spectantibus exculta fuit, qui 



Gravitatem (cum potentia manualis non sit) vix aliter 



I quam in ponderibus per potentias illas movendis con- 



siderarunt. . . ." 



i Rankine had this preface in his mind in preparing his 



inaugural address (1856), a "Preliminary Dissertation 

 on the Harmony of Theory and Practice in Mechanics," 

 prefixed to his treatise on Applied Mechanics. 



" In physics and mechanics the notions of the Greeks 

 were very generally pervaded by a great fallacv, which 

 obtamed its complete and most mischievous develop- 

 ment amongst the mediaeval schoolmen, and the remains 

 j of whose influence can be traced even at the present day 

 I —the fallacy of a double system of natural laws; one 

 theoretical, geometrical, rational, discoverable by con- 

 templation, applicable to celestial, ^therial, indestruct- 

 ible bodies, and being an object of the noble and liberal 

 arts ; the other practical, mechanical, empirical, dis- 

 coverable by experience, applicable to terrestrial, gross, 

 destructible bodies, and being an object of what were 

 once called the vulgar and sordid arts." 



We want in our theoretical treatises more of the spirit 

 expressed on the title-page of Hayes's Fluxions, 1704, 

 " A work very useful to those who would know how to 

 apply Mathematics to Nature." 



To do this we must come to close quarters, and 

 "missis formis substantialibus et qualitatibus occultis" 

 fire off the elegant artillery of analysis ; in fact, reduce 

 the formulas to their numerical applications ; it is in this 

 way only that the various differences so notable in the 

 NO. 1495, VOL. 58] 



mode of treatment in different schools can ultimately 

 become reconciled. 



Suppose we set up our author as the champion of the 

 first of these two schools of thought described above 

 by Rankine, and pit him against Prof. Perry, as the 

 champion mathematician of the engineers. 



The first point of dispute will be the measurement of 

 force ; the engineer will insist on retaining in Dynamics 

 the statical gravitational measure of force, considering 

 that he works in a field of gravity, practically uniform 

 over the surface of the Earth, on which the human race 

 is imprisoned ; and also because the gravitational 

 measure of a force is the only one capable of direct 

 experimental determination to the highest degree of 

 accuracy ; this is not the case with the absolute measure 

 of force, the one solely adopted in the demonstrations 

 of the present treatise. 



There are certain advantages in recording the re- 

 sults of cosmical, electrical, magnetical, and astronomical 

 results in absolute measure ; for if the author should 

 succeed in having his treatise adopted on another planet, 

 his C.G.S. units would be immediately applicable, on 

 the assumption of perfect astronomical observation and 

 measurement ; but for experimental verification each 

 planet would have recourse to its own gravitation system. 



A problem proposed recently in an American technical 

 journal, "to find the work required to lift the Earth one 

 foot," might perhaps serve a useful purpose in focussing 

 discussion between the merits of absolute and gravitation 

 measure. 



A curious note on the last page of this treatise dis- 

 misses the units in which all our engineering calculations 

 are carried out, in a few lines, such as — 



"Thus the equation which we write P = mf where P is 

 the force producing acceleration /in a body of mass ///, 

 could be written in these units P = {jn\g)f where g is 

 the same constant." 



" It does not tend to simplicity that the writers who 

 use these {i.e. the gravitation) units also use the word 

 'weight' for the quantity we call ' mass,' and the letter 

 W where we use ;«, and thus they write the above 

 equation P = (W/^)/." 



" Much confusion has thereby been produced." 



But Prof. Perry will retort by saying that the confusion 

 is produced by those writers who never have to employ 

 the theory they teach ; and that the words " frequently 

 not " should be changed to " never " in the statement 

 in § 299— 



"The C.G.S. system of units, although generally used 

 in scientific work, is frequently not employed in practical 

 applications of science." 



Such a thing as an arithmetical mistake is unknown 

 among those who work with gravitation units ; the same 

 cannot be said of the adherents of absolute measure 

 who are very apt to slip a ^ in their calculations (there 

 is a ^missing in the result of ex. 60, p. 75.) 



How does our author reconcile his definitions in 

 Chapter v. with the precise legal terminology of the Act 

 of Parliament on Weights and Measures ? — 



" The weight in vacuo of the platinum weight (men- 

 tioned in the First Schedule to this Act), and by this 

 Act declared to be the imperial standard for determining 

 the imperial standard pound, shall be the legal standard 

 measure of weighty and of measures having reference to 



