I848."l 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL.! 



SSf 



inclined at any an^le, Professor Moseley has shown that the 

 difference of the forces of compression and tension is equal to the 

 resultant of the applied forces multiplied hy the sine of the 

 an^le which it makes witli the normal to the neutral line at the 

 point of rupture.-" 



In conclusion, if your reviewer is right, it follows that Dr. 

 Mutton, Dr. Young-, Professor Barlow, Dr. Whewell, Professor 

 Moseley, Professor Wallace, Emerson, and Tredgokl, one and all 

 of them, must be wrong ; but I think that any reasoning man will 

 require something more, to convince him that the laboured demon- 

 stration of these men, who have hitherto justly been regarded as 

 high authorities on the subject, are false, than the mere denial of 

 an individual writer. Considering, then, with whom it is that your 

 reviewer is at issue, — not with Dr. Gregory and me, but with all 

 the first mechanical and mathematical writers who have lived, — 

 would it not have been wiser, had he assumed a little less positive 

 tone in his attempts to lay down the law ? 



I remain, &c., 



London, July 15, 184.8. Henry Law. 



* „.* Mr. Law cannot accuse us of want of good nature, for we print 

 his letter at full length. We had unoriginal ])reiudice against Dr. 

 Gregory's book. The author has a kind of celebrity from his position 

 at M'oolwich, and from having written copiously, which, though he 

 has not made a single step in the advancement of science, led us 

 to imagine him capable of compiling a book like the present with- 

 out gross and systematic blundering. The first two or three mis- 

 takes occasioned a little surprise, but were charitably attributed to 

 inadvertance. It was only slowly and reluctantly that we yielded 

 to the conviction, that the book was radically and essentially erro- 

 neous, and that a real mathematician could not by any chance 

 have written it. 



Still, we clung to the hope that Mr. Law was guiltless of the 

 various delinquencies to which he had given liis editorial sanction. 

 It was, at least, a good-natured excuse — a pious fraud, to delude 

 ourselves and readers with — that he had uttered false coin, not 

 well knowing it to be spurious. Alas! even this pleasing self- 

 delusion is destroyed. 



The various subjects of discussion are not questions of autho- 

 rity, but of reason. If Newton, Lagrange, and Laplace were to 

 arise from the dead, and assure us that they had discovered the 

 ordinary multiplication table to be incorrect, not even their united 

 testimony would produce conviction in our minds. M'^e may as 

 well set out by avowing, that if those illustrious names were 

 quoted in support of Dr. Hutton and Mr. Law. even they would 

 not produce the slightest change in our convictions. We should 

 feel perfectly certain that their words were misquoted, or strained 

 beyond their intended signification, or — (out it must come) that 

 they had lost their wits ! 



Our task is a very simple one as regards the definitions ; it is 

 to refer Mr. Law to books in which he will find them correctly 

 laid down. That Barlow, Hutton, and Young, have fallen into the 

 same mistakes as Dr. Gregory, only corroborates an opinion inde- 

 pendently arrived at — that they were just the men to do so. The 

 distinctions between the cycloid and the trochoid are given 

 correctly, and in exact accordance with our criticism, in Hall's 

 "Differential Calculus, and in page 137 of the "Examples on the 

 Differential Calculus," by the late D. F. Gregory, fellow of Trinity 

 College, Cambridge, one of the most profound analysts in Europe 

 — and therefore a very different mathematician to Dr. Gregory of 

 Woolwich. 



Professor Peacock, in Iiis cidlection of Examples on the Cal- 

 culus, distinguishes in a similar manner, between the cycloid and 

 trochoid. The other curves in question are thus defined by him, 

 page 192 :— 



** If one circle revolve iipon annllier as its base, and in (lie same plane 

 with it, it i> railed the Ejiitrocliinil, wliicli beromes the Epiviiildid when 

 the (iescrihinj; point is in the Circiiinference of tlie re^olviii;;; circle. If a 

 circle jeviilve in a similar inaiiner opon the coucuve part of ilie circunifer- 

 etic.e of anolier eiule, the curve de^criheri by a point iii its plane is called 

 X\\e Hil]iotrocltuid, which becuiiies the HijiiocyrluiU \\\:ea tliat poiul is iu 

 liie cireiinifei-etiee." 



The definition of equilibrium criticised by us, begins "When 

 forces that act upon a body destroy or annihilate each other's 

 operation, so that the body remains quiescetit " &c. If the 

 words " so that " have the meaning generally adopted by persons 

 who speak and write the English language, it is here asserted that 

 if the forces acting on a body destroy each other's operation, the 

 body must be at rest. It is wearying to have to repeat the cor- 



=2B Mecb. Friu. 0. i-uginejiiug a id Arcii., p. 4J^* 



rectioTi of so obvious a blunder, but we have again to tell Mr. 

 Law, that the case of uniform motion has been carelessly over- 

 looked by his author. On Dr. Whewell's authority, it is declared 

 that statical forces are called pressures; but he does not deny 

 what we asserted, that dynamical forces are called pressures also ; 

 .repeated instances of such a use of the expression, may be found 

 in his works. 



Dr. Gregory's assertion as to the manner in which Leibnitz used 

 the term ins viva, is said to be confirmed by Barlow and Hutton. 

 However, we need not inquire at second-hand what Leibnitz said, 

 or did not say, because his very words are quoted at length. Now, 

 does Mr. Law really mean to assert that in the Latin quotation 

 »>!> viva is called a force ? If so, all we can reply is, that he dis- 

 plays considerable fortitude under trying circumstances. 



The Latin quotation first specifies the cases in which the two 

 things called tiw mortua ani vis viva respectively exist — the former 

 where there is no motion, and the latter where there is motion. 

 Then it is added, that " where a body has been some time falling, or 

 a bow has been some time unbending itself, or in any similar case, 

 there is via viva, generated from the continued infinite impressions 

 of vii mortua," — a perfectly distinct recognition of the truth which 

 we assei'ted, that vis viva is not force, but something generated by it. 

 Of course, the true interpretation of the phrase must be obtained 

 from the context — not from an arbitrary translation of the word 

 vis, which has a great diversity of meanings. 



Professor Moseley's statement of the principle of ««*■ viva is so 

 clear, that it is really marvellous that Mr. Law did not perceive 

 that he quoted an authority decisive against him. He says vis 

 viva is a force ; Moseley, that it is equal to a certain amount of 

 work of forces : " work" being pieviously explained to be the pro- 

 duct of force and distance. It is also important to remark, that 

 vis viva is not said to he work, but to be equal to work. Twenty 

 shillings are equivalent to a sovereign, bMt they are not a sovereign, 

 but difler from it iu weight, size, colour, and almost every other 

 particular, except current value. 



We will follow the example of printing the contradictory state- 

 ments side by side. The case then between the authority last 

 quoted and our present correspondent, stands thus : — 



Mr. Law. 

 viva of a bmly 



Vis viva of a bmly " is the 

 WHOLE mechanical effect which it 

 will produce ia being brought to a 

 state of rest." 



Professor Moseley. 

 ** The dilferenee betweeo the ag- 

 jjregale work of the accelerating 

 forces of the system and that of the 

 retdrding forces is equal to one- 

 half tlie risvira accumulated or lost 

 in the system." 



The discrepancy between " the whole" in the one quotation, and 

 the "one-half" in the other, would be a fatal objection to Mr» 

 Law's views if no other existed. 



The following definitions, in which, be it observed, "force" is 

 not even mentioned, are conclusive as to the use of the phrase vis 

 viva among modern mathematicians :— 



"The ris rica of a particle is the product of its mass and the square 

 of its velocity." — Karnshaw's Dynamics, page 177. 



** Since the publication of D^AIemberv's work, the term ris rira has 

 been used to signify merely the algebraical product of the mass of a 

 movin;; body and the square of its velocity." — Walton's Mechauicat 

 Problems, page 3»7. 



"the sum of .11 the bodies of a system each multiplied into (he square 

 of its velocity is called the ris rivii of the system." —\Vliewell'& Elemea- 

 tary Treatise on Mechanics, page 292. 



" The term vis viva is slili used to express the product of the mass and 

 the square of the velocity." — Pratt's Mechanical Philoscipliy, page 202. 



" l)u appelle/oite vive d'un point materiel, ou, plus j;e .^lalement, d'un 

 corps donl tons les poin's onl les meme vilesse, le produitdeson masse par 

 le cane de celte vitesse." — I-'oisson 'I'lait^ de IM^caniqiie, (oiii. if., page 29. 



The proposition respectingtie-beams was condemned by usbecause 

 some of the forces acting on the beam and strut areneglected ; and we 

 showed as corroboratory proof of the incorrectness of the solution, 

 that it led to an absurdity. Of all tliis our correspondent takes 

 no notice ; but refers us to Professors Moseley and Whewell. If 

 both these references were relevant, which they certainly are not, 

 they would not justify a palptible and obvious error ; and we must 

 tell Mr. Law plainly, that we should have had far more respect 

 for hiin as an opponent, if he had made the necessary correction, 

 instetul of endeavouring to transfer the blame to authorities no 

 way involved in it. As for Professor Wallace's adoption of the 

 problem, we can only say that in this instance he has made an un- 

 forttinate selection. 



By inserting the word "uniform," in quoting our remarks upon 

 page 193 of the " Mathematics tor Practical Men," Mr. Law 

 makes us talk nonsense. However, we freely admit that we hei& 



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