362 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



[Nov. 



at time /, the velocities of A and B previously to impact being sup- 

 posed contrary in directioii. Let r = 6 be the value of z when the 

 spring has reached the limits of ils compression ; z then is a miui- 



dz 

 mam, • . -r-, ^^ o ; 



at 



dx' dx 

 .•. \\ X -\- z = X , -r- = -r- • 

 ^ dt dl 



If, now, the spriiig has no power of recovery — /. e. if the force T, 



dx 

 ceases, the balls vtill move on together with equal velocities, — and 



dx' , dx / T , dx 



— . Also — = u — / - dt; -— 

 dt dl J A dt 



s being the velocity of B previous to impact 



dx / T dx' /'T 



— - u - - dt\ — — -v\ I - dt; 

 dt J A dt J K 



velocity of B previc 

 . eliminating the I T dt. 



(B + AJ 



dx 

 ' dt 



= Au — Bv. 



This is the formula for the impact of what are generally termed 

 bard, inelastic bodies — i.e. bodies of which the particles have no ten- 

 dency to restitution after displacement. If, however, after -y^ =: o 



the spring recoils with perfect elastii'ity, the integral I — dt during 



the time that z increases from z ^^ h io z ^ a, will = 



J A 



dt taken 



during the time z decreased from z 



/'T dx 



hat / - dl = u - —■ = 

 J A dl 



••. the final velocity of A will be 



a to z := b; 



Au - Bv 



B (u + r) 

 A-f B ' 



A + a 



which is the formula for the collision of perfectly eUistic bodies. 



The most important part, however, of the "Mathematical Physics" 

 is that in which the author developes his theory of heat and the mo- 

 lecular constitution of gases; and it is but justice to him to observe 

 that much of the first part of his work is confessedly a juvenile pro- 

 duction. Whether his investigation of tlie motion of a crank, in 

 which he has fallen into the common error of neglecting the mass of 

 the connecting-rod, is to be reckoned among his youthful performances 

 or not we cannot say, — we trust, however, for the author's credit, that 

 it is. We now come to the theory of heat and the constitution of 

 gases: — Newton conjectured that heat might arise from an intestine 

 motion of the particles of matter, and that temp.'rature might vary 

 as the velocity of the particles. Mr. Herupath, on the other hand, 

 supposes the temperature to vary as the momentum of the particles; 

 and combining this theory with his idea of the perfect hardness of the 

 particles — or rather, as we should say, their perfect elasticity — he 

 shows very clearly and beautifully how the pressure of gases varies 

 with their temperature ; and how the specific heat of bodies multi- 

 plied Ijy their chemical equivalents is constant. There are, hoviever, 

 many phenomena of heat, which appear to us utterly incapable of 

 explanation on Mr. Herapath's theory; — we allude to radiation, con- 

 duction, and politrization. How is it that bodies which radiate the 

 best conduct the worse, and vice versti? And how are we to account 

 for the intricate phenomena of polarization? Surely these facts de- 

 pend on something more than a lawless motion of the particles of 

 matter among themselves. That the particles of matter, or the 

 nuclei of material forces, are continually in motion is higlilv probable 

 — nay, almest certain ; but what that motion is — on which heat, light, 

 and electricity, with all their varied yet definite phenomena, depend 

 — remains yet, we think, to be discovered. 



Various theories of the molecular constitution of matter have, in- 

 indeed, been put forth from time to time, — none, however, that merit 

 much attention, with the exception of the undulatory theory of light; 

 and even in this, the great result arrived at — viz. the form of the 

 wave surface, — although it satisfies most, and has suggested some 

 facts of polarised light, is deduced from considiTations dvnamicallv 

 unsound. We may here observe that Fresnel (see "Airy's Tracts," 

 p. 357), in determining theoretically the polarising angle of a reflect- 

 ing sur^ace, has adopted a hypothesis for the motion of the particles 

 of ether nearly the same as that of Mr. Herapath. 



In conclusion, we cordially recommend the work to those of our 

 readers who have sufficient leisure and mathematicid knowledge to do 



justice to the author, though we cannot help expressing a wish that 

 Mr. Herapath had devoted half the time and ability to the mathema- 

 tics of engineering that he has to the castle-buililing of hypothetical 

 speculations, and we might then have had the pleasure of reviewing 

 a work of less pretensions but of far more solid usefulness. The 

 most ])rofuund mathematicians of the day with whom we have had 

 the honour of conversing on the subject, shrink from the dithculties 

 attending all theories of molecular constitution, and in their wildest 

 dreams we believi' have never so much as dared to hope for a solution 

 of even one of those grand mysteries — " Heat, Gaseous Elasticity, 

 Gravitation, and other great Phenomena of Nature." 



Railway Locomotion and Steam \avigalion : their Principles and 

 Practice. By John Curr, of New South Wales, London: Williams, 

 1817. Svo., pp. 181. 



" Oh that mine adversary had written a book," cried Job in bitter- 

 ness of spirit. We, who are not nearly so patient as lie, are induced 

 by the perusal of the work before us to exclaim — Oh that mine adver- 

 sary had to review a book ! Mr. Curr has come all the way from Nevr 

 Souih Wales to have his hark and his bite at modern engineeiing .' A 

 man does not travel Iti.OiJtJ milts for a trifle; and accordingly Mr. 

 Curr bow-wows pretty loudly. 



First, our excellent contemporary, the Jilechanics' Magazine, comes 

 in for a snarl. Froin "a careful examination of two volumes and two 

 odd numbers" of that work, our author is satisfied that " the present 

 actual and scientific knowledge of English engineers" is in a most 

 deplorable condition ; and so in order to enlighten them he resolved 

 on quitting "a peai.eful homestead in the fair clime of Australia," 

 embarked on board the good ship " St. George," for England, arrived 

 safely, and forthwith published the present volume. It is our private 

 conviction that Mr. tjurr is the coming max who has been so lung aud 

 so anxiously expected. 



To attempt an intelligible analysis of his doctrines were as vain as 

 to essay a systematic arrangement of the Sibylline leaves, or an inter- 

 pretation of the oracular teachings of a Pythonissa. Science and satire, 

 analysis and adventure, are so strangely intermingled that dim mortal 

 vision frequently misses the line of demarcation. Jlr. Curr sets off 

 with a grave bit of theory about motion of fluids, or a pet doctrine of 

 gravitation, and interrupts himself to tell a personal anecdote. As 

 many "most disastrous chances of moving accidents" have befallen 

 him as Othello, and they are set down in this book, in the very thick 

 of philosophical propositions and algebraical symbols. Our author 

 seems to entertain the idea of combining the truths of science with 

 the " intense interest" of a melodrama. B'or example, he begins to 

 talk about latent heat, and suddenly stops to tell a startling story of 

 his father being on a certain occasion "reduced to the necessity of 

 concealment in a wood for three days and nights to escape the fury of 

 the populace." In another place, he records a dispute between him- 

 self and somebody at Norwich, which somehow or another induced 

 him to go to Margate, where he "issued through the town a printed 

 placard," &c. Further on he tells us that his father was disowned by 

 his grandfather on accountc' a difference of opinion on engineering 

 subjects, "and the letter to ihat effect was retained in his family for 

 thirty years or more." Our author is as rich in family anecdotes as in 

 scientific discoveries, and passes from the one to the other with sur- 

 prising facility. Every reader of Hudibras knows that 



'* Tti' adventure uf tlie bear aud fiddle 

 Is sung, but breaks off in tlie middle.'* 



But the excursions and imaginative flights of the political satirist, 

 Butler, are nothing to those of the pliilosophical satirist, Curr. 



Poor Doctor Ilutton comes in for a more than ordinary share of 

 abuse. Various errors and inconsistencies in his theoretical views 

 are pointed out. Huttoii wrote at a time when the principles of me- 

 chanics, and especially the practical application of them, were much 

 less understood than at present : and we are quite ready to accord to 

 Mr. Curr the easily-aequired merit uf having proved that Huttoii is 

 not iiilallible. Ue was a much better arithmetician than mathemati- 

 cian, but the time at which he wrote may excuse some of his inaccura- 

 cies — and it is but a pious task to avenge his memory by showing that 

 his antagonist commits errors equally grave without the same excuse 

 fur them. For instance, Mr. Curr propounds various formula for cal- 

 culating the motion of railway tiains, assuming the modulus of friction 

 to be constant; whereas the evidence of uniform experience shows 

 that tile r(sistance to the motion of the wheels on the rails increases 

 very rapidly with increase of velocity. The percussions in passing 

 over the joints of the rails, and the vibrating motion of the rails them- 

 selves, render necessary a great expenditure of power. Aud us these 



