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THE CIVIL ENGINEER AND ARCHITECrS JOURNAL' 



I Jbiy, 



chanics. AVhat will our mathematical readers say of such a defini- 

 tion as the following ? 



" Whca the forces that act upon a hody, destroy or annihilate each other's 

 operation, ao that the boily remains quiescent, they are said to he in equili- 

 brium, and are then called pressures." 



This is clumsy and incomplete, to say the least. It is assumed, 

 th:it when two forces "annihilate each othei''s operations," tlie body 

 is at rest, — the case of uniform motion is overlooked. Besides, the 

 word pressure is restricted to statical forces, whereas it is properly 

 applied to dynamical forces also. 



" f'is viva, or liiing force, a term used by Leibnitz to denote the force or 

 power of a body in motion ; or the force which would be required to bring it 

 to rest." 



Leibnitz never did anything half so absurd as is here said of him. 

 Vis viva is not a force (or power, — for Dr. Gregory previously 

 states that the words force and power are synonymous). Vis viva 

 is a mere technical phrase — signifying, simply, mass multiplied by 

 tlie square of velocity — which Dr. Gregory and his editor are 

 determined to distort into something very complicated and abstruse. 

 So far from vis vim being a force, it is not even measured by force 

 alone — another element being the distance through which the 

 force acts. When a hody is acted upon by only one uniform force, 

 the vis viva generated is equal to twice the force multiplied by 

 the distance described in the direction of the force. 



In the second problem of the chapter on Statics, the calculation 

 respecting the str<ain on tie-beams and struts is totally erroneous. 

 It is not worth while to state the problem here, as we could not 

 make it intelligil)le witliout the diagrams. To the reader wlio has 

 the work before him, it will be sufficient to state that the error 

 ai'ises from considering tlie forces at one end of the strut and tie- 

 beam, and neglecting the forces at the other end of each. The 

 conclusion is manifestly erroneous, for when the tie-beam became 

 indefinitely long, it would be vertical, and the tension equal to the 

 weight suspended ; the strain on the strut at the same time he- 

 coming zero. 



" If the particles or bodies of any system be moving uniformly and recti- 

 lineally, with any velocities and direction, the centre of gravity is cither at 

 rest, or moves uniformly in a right line." 



This is not true. Does the author mean to assert, that if two 

 bodies be moving witli different velocities in straight lines perpen- 

 dicular to each other, the common centre of gravity moves in a 

 straight line .'' 



In discussing the pressure of earth against walls, the line of 

 rupture and the natural slope are said to be synonymous — they are 

 entirely different things ; the line of rupture being that which 

 defines what is technically termed the wedge of ma.xinmm pressure. 

 In the next paragraph is discussed the pressure exerted against 

 the wall by the prism resting on the natural slope ; whereas, by the 

 very definition of natural slope, that prism e.verts no such pressure, 

 the friction being of the exact amount necessary to sustain the 

 weight. 



The section on the stability of the arch discusses the conditions 

 for a case of rupture which is mechanically and geometrically im- 

 possible — that where there are only two joints of rupture, equi- 

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

 incapable of sliding. In the last of the formulje in this section, 

 the right-hand side of the equation has double it proper value. 



The preliminary part of the chapter on Dynamics has been re- 

 written, — not however, as we think, with great success. The confu- 

 sion of ideas respecting vis viva is really marvellous, considering 

 how simple the real signification of the phrase is. i\Ir. Law says, 

 first, " Mechanical effect is measured by the product of the mass or 

 weight of tlie body iuto the space over which it has moved." Then 

 he defines the vis viva of a moving body as " the whole mechanical 

 effect which it w ill produce in being brought to a state of rest." 

 This definition is by no means satisfactory, p'irst, the mass or 

 weight are spoken of as convertible terms. Next, coupling the 

 two definitions, the vis viva is said to " produce" the mass or 

 weight multiplied by the distance. This is a strange expression : 

 however, if we leave out the word " mass," and for " distance" 

 read " twice the distance," the idea intended to be conveyed is 

 tolerably correct, where the motion is vertical and the only force 

 is that of uniform gravity. For bodies acted on by variable force, 

 and for curvilinear motion, the definition is totally inapplicable. 



In jilace of an enunciation of the three laws of motion, we have 

 the following experiments as the foundation of dynamics. 



" From carefully conducted and often-repeated experiments, the following 

 results with regard to bodies in motion have been obtained : — 



" I. If a body of a certain weight, and moving with a given velocity, meet 

 another body of double that weight, and moTing with half the velocity, the i 



two bodies will destroy each other's motion, and both will be biought to a 

 state of rest. 



" II. A body of a certain weight and moving with a given velocity, being 

 subject to a uniformly retarding force (i. e, a uniform force acting constantly 

 in a contrary direction to the body's motion), will move over a certain space 

 in being brought to rest, and will occupy a certain time in doing so; then 

 another body of the same vxcight, hut moving with haf the velocity of the 

 former, being subject to the same uniformly retarding force, will move over 

 one quarter of the space moved over by the former, in being brought to a 

 state of rest, and will occupy in doing so half the time. And another body 

 of the same vseight, but moving with one-third of the velocity of the first, 

 will move over one-ninth of the space, and occupy one-third the time of the 

 first, in being brought to a state of rest." 



The second experiment would be analogous to that of trying 

 whether all points in tlie circumference of a circle possess the 

 property of equidistance from tlie centre ! It is a matter of defini- 

 tion that they should do so. In the same way, the mere definition 

 of uniformly retarding force leads to the inference here indicated 

 as the result of numberless experiments. The conclusion depends 

 on mere geometry, not on any law of mechanics. If a horse set off 

 at a constantly diminishing speed — 50 feet tlie first second, 49 feet 

 the next, 48 feet the next, and so on — it requires no knowledge of 

 mechanics, but a simple arithmetical computation, to ascertain how 

 far he has gone, and tlie time which has elapsed, when his velocity 

 is reduced to 20 feet a second. In the same way, if a body be acted 

 upon by a uniformly retarding force — that is, one which diminishes 

 the velocity at an assigned uniform rate — the law of motion is 

 assigned a priori, and it requires no experiment to determine the 

 distances corresponding to subsequent rates of velocity. The rule 

 that the distance traversed before the body comes to rest is pro- 

 portional to the square of the velocity destroyed, depends on purely 

 geometrical computation. 



In the section on Motion on Inclined Planes, we find the follow- 

 ing:— 



" Each particle of matter in a rolling body resists motion in proportion to 

 the square of its distance from the axis of motion." 



There is no such resistance, either in proportion to the square of 

 the distance from the axis of motion, nor in any other proportion. 

 It is incorrect to say that matter resists motion ; it neither resists 

 nor assists it, but is perfectly impassive and inert. The force of 

 inertia, as M. Poisson observes, is an incorrect phrase, arising from 

 inaccurate notions of the properties of matter — it, in fact, implies 

 an idea that matter has some inherent property of altering its own 

 motion. 



In the section treating of Pendulums, it is asserted, that if a 

 body suspended from a fixed point by a flexible string be made to 

 vibrate, it will always rise the same vertical distance as it has 

 descended. This is of course true when the motion is not dis- 

 turbed ; but it is added, that if the motion of the string be inter- 

 cepted by a projecting peg, so as to shorten the radius of the arc in 

 which the body moves, the same property holds. That this is not 

 generally true is obvious, from the consideration that the peg may 

 be so near the vibrating body, that the radius becomes too short to 

 allow the body to regain its original height. Moreover, the string 

 receives a jerk ; and therefore, unless it be perfectly elastic, there 

 is a loss of vis viva. 



After a confused and inaccurate definition and table of values 

 of the radius of gyration for several bodies, we have the following 

 lucid explanation of the principles of rotation : — 



" If the matter in any gyrating body were actually to be placed as if in 

 the centre of gyration, it ought either to be disposed in the circumference of 

 a circle whose radius is R, or at two points R, R', diametrically opposite, and 

 each at a distance R from the centre." 



All that can he made out of this is, that if tlie body be in one 

 place, it "ought to be" in another. The only inference from such 

 a statement is a querulous determination on the part of the writer 

 to be dissatisfied with the position of the body under all circum- 

 stances. The feeling is that of the wolf toward the lamb in the 

 fable — a general disinclination tliat the body should have anp 

 position. Several preceding sentences gave rise to the suspicion 

 that the author did not clearly understand the subject on which lie 

 was writing — the sentence just quoted converts suspicion iuto cer- 

 tainty. 



The following are the definitions at the commencement of a 

 chapter on Central Forces : — 



" (1.) Centripetal force is a force which tends constantly to solicit or to 

 impel a body towards a certain fixed point or centre. (2.) Centrifiuj at force 

 is that by which it would recede from such a centre, were it not prevented 

 by the centripetal force. (3.) These two forces are, jointly, called central 

 forces." 



Centrifugal force is not, as here stated, directed towards a fixed 

 centre. It is normal to the path of motion; and, therefore, there is 



