mo 



THE CIVIL ENGINEKR AND ARCHITECrS JOURNAL. 



LAuouOT, 



"pressures;" for wliicli, however, in addition to that of Professor 

 Moseley, I'have tlie autliority of Dr. \V"hewell,' mIjo says, 

 " ■S7a/ica' forces are called /(rraswre.v ;" and Dr. Youup," who says, 

 " A pressure is a force eonuteruclKd hi/ anutkerfiirce, so that im motion 

 is produced." If, then, your reviewer is correct, it follows that 

 Professor Moseley, Dr. Whewell, and Dr. Young are wroiiii. 



Your reviewer next takes up the subject of vis viva, on which I 

 «ay, — 



•' Vis visa, or living force, a term used by Leibnitz to denote tlie/oree or 

 power of a boily in motion; or the force which would Ite required lo l)ring 

 it to a btate of rest." p. lOS 



Professor Barlow says : " Vis viva, or living; force, is used by the same 

 aullior [[.fihniiz] to denote Ihe/orce or power of a body in motion."" 



Dr. llutton says : " I'is mortua, and Vis viva, are terms used by Leibnitz 

 and Ids followers (or force ; understanding l)y thf; latter, that force or 

 power of acting which resides in a body in motion."'" 



Notwithstandiner, however, the united testimony of Professor 

 Barl()w, Dr. Gregory, and Dr. llutton, that Leibnitz used the 

 term vis inra as here stated, your reviewer is ])erfectly sceptical 

 upon the point, and boldly asserts "that Leibnitz never did 

 anything half so absurd as is here said of him ;" that he did do so, 

 is however a matter of fact, for here are his own words : — 



" lline Vis quoque duplex : alia elementaris, quio et mortimm apello, 

 quia in ea iiondum existit motus, sed taniiitn solUcitatis ad niotum, qualis 

 est glubi in tulin, aut lapidis in funda, etiam dum adhuc vinculo tenetur ; 

 alia veTo vis ordinaria est, cum niotn actual! ennjuncta, quara voco vitam. 

 Et vis mortnse qoidem cxemplura est ipsa vis centrifuga, itemque vis 

 gravilatis, pen centripcta; vis etiam qua elastrum tensum se restituere 

 incipit. Sed in percussione, qnse nascitur a gravi jam aliquamdiu cadente, 

 aut ab aruu se aliquamdiu restitue ite, aut a sinuli causa vis est viva, ex 

 infinitis vis mortua; impressionihus continuati? nata. Et hoc est quod 

 Gnlilieus voluit. cum oenigmatiea Inquendi lalione percussionis vim infinitam 

 dixit, scilicit, si cum simplice gravitatis nisu comparetur. Etsi autem 

 impetus cum vi viva semper sit conjunctus, differre taraen hoec duo, infra 

 ostendetur."" 



Not content, however, with denying that Leibnitz said that, 

 whicli his own works prove that he did say, your reviewer denies 

 that vis viva is a force at all, and says that it is a mere technical 

 term ; Dr. Whewell, ' - however, says, " The vis viva of a body in 

 motion is a force;" and Profe.=sor Moseley,'-' " That the difference 

 between the aggregate work of the accelerating forces of the 

 system, and that of the retarding forces, is equal to one-half the 

 vis viva accumulated or lost in the system." Therefore, either 

 your reviewer is wrong, or else both Dr. Whewell and Professor 

 Moseley. 



He next states that, "in the second problem of the chapter on 

 Statics, the calculation respecting the strain on tie-beams and 

 struts is totally erroneous;" to which I answer that the calculation 

 w correct, and that your reviewer is tvrnng ; as he will iind if he 

 refers either to Tredgold,"* Dr. Whewell,'-^ Professor Moseley, "^ 

 or Professor Wallace," (who quotes from Dr. Gregory the vei-y 

 prolilem denounced as incorrect J. 



Your reviewer then extracts the following proposition relating to 

 the centre of gravity : — 



" If the particles or bodies of any system be moving-, 

 uniformly and rectilineally, with any velocities and di- 

 rections whatever, the centre of gravity is either at 

 rest, or moves uniformly in a right line " p. 193 



Emerson says : " If two or more bodies move uni- 

 formly in any given directions, their common centre of 

 gravity will either be at rest, or move uniformly in a 

 right line."'" 



Dr. Whewell says: "If there be several bodies, 

 whii'h either all attract and are attraeted iiy a sinele 

 b( dy, or all attract each other, these also will move in 

 suili a manner that the common centre of gravity 

 will cither remain at rest, or move uniformly in a 

 straight line."'" 



He then asks a question ; " Docs the author mean to assert, 

 that if two bodies be moving with dift'ereiit [uniform] velocities 

 in straight lines perpendicular to each other, the common centre 

 of srnvitv moves in a straiirht line?" To which I answer very 



^ i'.Kriiiciiiitiy I'lC'iliiit: uii AleL'Uuiiics, p. ti. 

 s A course of Lei-tures on Nat. Phil., vol. 2, p. 37, 

 9 Nfiv Math, and I'hil. Dictionary,— Art. " Vis." 

 ' « ritil. antl fllalh. Dictioniiry, vol. 2, p. -'(liH. 

 11 (i. G. Leibiiitzii. Opera Omnia, toni. ;i p. ;U8. 

 -J^ MeL'haiiifsof KiiMint^rinK. p. 192. 

 18 MeCh. Piia.of EnguieerinB and Arch., p. 133. 

 14 Klementary IVincipleii ot Carpthtry. p. i*. 

 »s Eleminlary Treatise on Meclianies., p. y4. 

 ifl RlCLh Prin.of Kngitieering iOfl Arch., ;j, 424 

 17 Practical Knginefr's I'oLket Guide, p. 17. 

 1 n Piinc'pWs ol Alcctiunics, p. fi6. 

 •^O On Ihe Free Mutiun ol Puiuls, p. 90. 



Your reviewer 

 • merely says: " This 

 is not true." 



decidedly, " Yes, I do ; and if you are at all .sceptical upon the 

 point, if you refer to Emerson's ' Principles of JVlechanics," p. 67, 

 you will find the truth of my answer demonatrated." 



The next objection of your reviewer is to my use of tl)e term, line 

 of rupture; which, liowever, I prefer to apply to the actual case of 

 rupture of the ground, which takes place when the wall falls, and 

 which is then obviously the same as the natural slope : the line de- 

 termining the wedge of maximum pressure is only an imaginary 

 line, and not that on which the ground would really separate. 



Your reviewer has quite misunderstood Dr. Gregory, when he 

 asserts, that the conditions upon which he examines the stability 

 of an aridi, are '" that there are only two joints of ru])ture, e([ui- 

 distant from the crown, the loading symmetrical, and the piers in- 

 capable of sliding," no such conditions being assumed, or indeed 

 necessary. 



The next paragraph of your reviewer requires no comment from 

 me ; the obvious mis-quotation of my words does as much violence 

 to common-sense and grannnatical construction, as it exhibits the 

 desire to pervert tlie meaning of what I actually say. 



He then states that I have given certain experiments (which 

 he extracts) " as the foundation of dynamics" and " in place of 

 an enunciation of the three laws of motion," which is not the fact: 

 I have merely employed them to illustrate the necessity of re- 

 garding time in estimating the forces of moving bodies : see 

 Atwood,"" Barlow,-' and Hutton.-^ 



Your reviewer next linds fault with my using the expression, 

 " Each particle of matter resists motion ; is he aware that Dr. 

 Whewell--' repeatedly uses a similar expression — "the inertia of 

 the particles to resist the communication of motion ■" and 'that M. 

 Poncelet, in the introduction to his Mccanique Industrielle, has re- 

 vived the term ris inertiee, and has associated with it the defini- 

 tive idea " of a force of resistance opposed to the acceleration or 

 the retardation of a body's motion." 



Your reviewer next takes objection to the assertion, that (neg- 

 lecting the effects of friction) if a body suspended from a fixed 

 point by a flexible string, have its path altered by a projecting 

 pin, it will rise to the same height as it would have done if not so 

 intei'fered with ; Dr. Young, however, speaking on this subject 

 says : " We may alter the form of the path in which it descends, 

 by placing pins at different points, so as to interfere with the 

 thread that supports the ball, and to form in succession temporary 

 centres of motion; and we shall find in all cases, that the body as- 

 cends to a height equal to that from which it descended, with a small de- 

 duction on account of friction."'-* 



After stating that Dr. Gregory's definition of the centre of gyra- 

 tion is "confused and inaccurate," although identical (as he will 

 find by reference) with that given by Dr. Hutton,*'* by Emerson,^* 

 and by Professor Barlow,-^' he proceeds to show by reference to the 

 ^^ fable of the wolf and the lamb" that one of the propositions re- 

 lating to the centre of gyration cannot be correct, and arrives at 

 the certain conclusion that the author (as also Emerson, from whom 

 the same proposition is takeii) did not clearly understand the 

 subject on which he wrote : — 



Etnerson's Proposition, 

 " If the matter of any gyrating 

 body were actually to be placed in 

 its centre of gyration, it ought 

 either to be disposed of in the cir- 

 cumference of a circle, whose radius 

 IS S 0, or else into two points, dia- 

 metrically opposite, equal and equi- 

 distant from S."-" 



Proposition Criticised. 

 " If the matter in any gyrating 

 body were actually to lie placed as 

 if in the centre of gyration, it ought 

 either to be disposed in the circumfer- 

 ence of a circle whose radius is R, 

 or at two points R, R,' diametrically 

 op]iosite, and each at the distance 

 11 from the centre." p. 230. 



Your reviewer next informs us that centrifugal force is not 

 always "directed towards a fixed centre," in which I perfectly 

 agree with him, and am not aware that any person has stated 

 the contrary. 



He then points out an error of Dr. Gregory's, relating to fly- 

 wheels, which had escaped my observation, and one of my own, in 

 equation (I) page .'i7:i, which' sliould read \ LP, = E(5 + A); but 

 which fortunately does not aft'ect any other part of the subject. 

 He then states that the total forces of longitudinal compression 

 and tension are equal and opposite ; this i.s, however, only the 

 case when the apjilied forces are perjiendicular to the beam, for when 



20 A Treatise on the Itectilinear Motiirn and liotation of B«idieSi p. .*i5. 

 2 1 New aiuth. and Phil. Oittionary, — Art. "Force." 



22 Phil, and fllaih. Pictionavy, vol. I, p. .')3.'5. 



23 Itlechiinlcs ol Knglhceriiip, p. 13i. 



24 A course of Lectures on Nut. Phil., vcl. 1, p. 43. 



25 Phil, and Malh. IJictioiiary, vol. l,p. '_W. 



26 Principles ul' Altchtin C9. p HI. 



X7 New Math, and Phil. D.ciiunary.— Art. "Centre of Gyration ;" and Encydo- 



piedia filet ,— Art. "flle.h.nics," vol. 3, p. 134. 

 2 8 Priuciples of Mechanics, p. 83. 



