VELOCITY. 



VELVET. 



that we do not think it necessary to lengthen thu article by dwelling 

 upon it. Two of a sort, whether velocities or accelerations, acting 

 upon ntie particle, at any one mutant, are equivalent to a third repre- 

 entod in magnitude and direction by the diagonal of a parallelogram, 

 the two aide* of which represent in magnitude and direction the two 

 component*. And by the law of motion which is commonly called 

 the second [MOTION, LAWS OF], the several accelerations which act 

 on any particle in n. ',im Hirertitmi may have their effects com- 

 puted separately without any error being introduced. If. then, sup- 

 posing a particle to move in a plane, the pressures P and q be applied 

 to it in the directions of the rectangular co-ordinates x and y, the mass 

 of the particle being u, we have 



equations which are only true on the supposition that there is this 

 connection between the unit of mass and that of pressure, namely, that 

 the Utter acting on the former during one unit of time shall odd to the 

 line which represents its velocity one unit of length. These equations 

 are enough to determine the equation of the curve In which the 

 particle must move, r and q being given functions of both rand y; and 

 the time of motion through any arc of the curve < is then found from 

 the following equation : 



r * - 



It is not here our business to proceed further with the consequences 

 of the definitions of velocity and acceleration ; but we must explain a 

 point which will arise in our subsequent article on VIRTUAL VELO- 

 CITIES. When wo have the means of actually ascertaining the motion 

 of a particle of given mass, that ia to say. of finding at every instant 

 its actual place, its velocities in the directions of its co-ordinated, and 

 its accelerations in those directions, we are prepared to assign the 

 pressures which must act upon it in those directions, at the instant we 

 are speaking of, either in mathematical units of pressure, as before 

 described, or, if the reader please, in pounds or ounces averdupois. 

 To show this, let us propose an instance, as follows : A particle whose 



weight (if weight were allowed to act) is 10 ounces, moves uniformly 

 along the arc of a parabola o P (whose focus is s, o s being half a foot) 

 at the rate of 2 feet per second : What pressures in the directions of 

 o H and s P (or of x and y) are necessary to keep up the motion ; and 

 in particular what are the pressures and the velocities at the point p at 

 which P = 3 feet ? The equation of the curve is 2y = X 3 , whence 

 we get 



dy rf 



Or the velocity in the direction of y is to that in the direction of .< 

 always as x to 1. 



But, being the arc OP, we have 



dt d& djc? dy* 



" W + d? =4 



4 dy> 4x* 



T5 5? ' 



df 



. 

 whence 



At the point in question y = 8, x* = 6, from which the velocities in 

 the directions of x and y are found to be -f* V()) and + W. or '7(6 

 and 1'852. We Uke the positive signs, since both motions obviously 

 tend to increase* their co-ordinates. Differentiate the last equations 

 again, and we have, 



dx d*x SJT dx_ dy_ <Py 8j dx 



Hi ~2? = ~ (\ -r a?)* dt ' 2 <5" dC ~ (!+**)' "3T 



<Px ix 



3? ' ~ (l+x*? 



(1 +*)' 



or the velocity in the direction of x is always retarded, while that in 

 the direction of y is always accelerated. And at the point in question 

 we have -4 v/0-M and 4-M0 for the accelerations, say -200 and 



We hart not entered Into the diitinctlon of meanlnn between ponltlre ind 

 MfatlTe Telocllle* and acceleration!, ulnce the qoeation le s purely algebraical 

 OM, unnecessary to be treated here if the (Indent rally undenund algebra, 

 sad Impossible to be explained within oar limits to one who doe* Dot. 



082; by which we mean that if the pressures then acting in the 

 directions of x and y were allowed to continue uniform for one second, 

 they would alter the velocities in the direction of r and y from 756 

 aii.l 1 .-.'.i to -756--200 and 1'852 + -082. The weight of the particle, 

 if weight * were allowed to act, being 10 ounces, the pressures which 

 would produce the preceding accelerations are, in ounces 



10 10 4 



~ 82-19 (1+ S 82-19 (!+*)*' 



the pressures in the direction of x being in the direction from N 

 towards o. At the point in question these pressiures are '062 and 

 0255 ounces. 



The pressures thus derived from the motion which actually takes 

 place, by means of the accelerations >P.r : dt* and d-y : dt-, are usually 

 called the efftctirt forces ; and the name is very Appropriate, because it 

 is true that these must be the forces which do really act Different 

 pressures produce different accelerations upon the same moss ; or to 

 one acceleration there is but one producing pressure, the mau being 

 given. But it may happen that the forces actually impretted. or the 

 pressures actually employed, at the point F. may be very different 

 from those which just produce the motion that ia produced. Suppose 

 for example that the mass p were attached to the mass Q by the rigid 

 rod PQ without weight ; and suppose such forces to be applied at r and 

 Q as, whatever may become of q, cause r to move uniformly along the 

 parabola in the manner above described. We may assign an inlinito 

 number of different motions to q, and for each motion of q we may 

 assign an infinite number of pressures which, being applied to P and q, 

 will give the two their supposed motions. But in no one of these 

 cases can the total amounts of pressure really applied to p, in the 

 directions of x and y, be any other than those which are calcu- 

 lated above : whatever may be the pressures actually applied at r. 

 the thrust or pull, as the case may be, of the rod pq, will supply 

 is necessary to make all the forces that act on p (those directly applied 

 and that arising from the said thrust or pull) together equivalent to 

 the pressures above calculated. This is the foundation of 1/Alembert't 

 principle. [FORCES, IMPRESSED AND EFFECTIVE ; VIRTUAL VELOCITIES.] 



The connection between velocity and pressure is not only obscured 

 by phrases as cloudy as " moving force, but also by the use of the 

 unit of mass instead of the unit of weight. This measurement by 

 masses instead of weights is so convenient and so desirable on rational 

 grounds, that it cannot ultimately be dispensed with ; but at the first 

 outset the student should be taught to reduce the new mode of 

 proceeding into terms of that with which he is then better acquainted. 

 A beginner in the theory of gravitation is not allowed to have the 

 least idea of the amount of the attractions of the several bodies upon 

 each other in pounds or tons, or any other unit which he can at once 

 understand. And we should not be surprised if many who can easily 

 compare the sun's attraction upon the earth with the earth's attraction 

 upon the moon, so as to find either of them when the other is given, 

 would be awkward at, if not actually puzzled by, the question of 

 comparing either of them with the weights in a grocer's shop. 

 Undoubtedly there would not be much of astronomical utility in the 

 question ; but for clear conception of the meaning and mode of 

 derivation of mechanical results, nothing can be of more importance 

 than the actual comparison of all results with those which ore best 

 known, because actually felt and perceived. 



VELVET, a variety of manufactured silk, remarkable for the soft- 

 ness of its surface. Velvet was unknown at least several centuries 

 after the introduction of plain woven silks ; and it is not mentioned in 

 any documents earlier than the 13th century. For a long time the 

 manufacture was confined to Italy, where, particularly in Genoa, 

 Florence, Milan, Lucca, and Venice, it was carried on to a great extent. 

 It was subsequently introduced into France, and brought to great per- 

 fection. On the revocation of the Edict of Nantes, in 1685, this branch 

 of weaving was begun in England by the refugees. 



The peculiar softness of velvet is owing to a loose pile or surface of 

 threads, occasioned by the insertion of short pieces of silk thread 

 doubled under the shoot, weft, or cross threads. These stand upright 

 so thickly as entirely to conceal the interlacing of the warp and shoot. 

 The richness of the velvet depends upon the closeness of the pile- 

 threads. The insertion of these short threads is effected in the follow - 

 ing manner : Instead of having only one row of warp-threads, which 

 will be crossed alternately over and under by the shoot, there are (too 

 sets, one of which is to form the regular warp, while the other is to 

 constitute the pile ; and these two sets are so arranged in the loom as 

 to be kept separate. The quantity of the pile-thread necessary is very 

 much more than that of the warp-thread; and, therefore, must be 

 flipping to the loom by a different agency. If the pile-threads were 

 worked in among the shoot in the same way as the warp-threads, 

 the fabric would be simply a kind of double silk, but without any 

 pile. The pile- threads are, therefore, formed into a series of ]<>>]>*, 

 standing up from the surface of the silk, and by subsequently cutting 

 these loops with a sharp instrument, the pile is produced. The loops 

 are formed in a very singular way. After the weaver has thrown the 

 shuttle three times across, making the shoot interlace three times 



The weight h been throughout nuppoeed to be neutralised, at it would be 

 11 the parabola were In the plane of s table, on which the particle is bid. 



