Notices respecting New Books. 63 



doubt that these illustrations alone will cause the book to have, as 

 it undoubtedly deserves to have, an extensive circulation. 



It will be evident from the large number of contrivances men- 

 tioned in the above list, that the description of each must be brief, 

 and that the attention of the reader is mainly directed to the dy- 

 namical principles involved in their use. It could scarcely fail to 

 happen, under these circumstances, that in some cases points in 

 the contrivances are not quite so fully described as the reader 

 might wish. In others the contrivance is regarded from a point of 

 view which does not bring quite the whole subject under notice ; 

 and this is sometimes a little misleading. For instance, the con- 

 trivance for feeding a running train with water is considered 

 simply as an illustration of inertia ; and this probably accounts for 

 the statement that the water which runs up the tube "is at rest 

 except so far as the movement in a vertical direction is concerned " 

 (p. 49). As one end of the tube is vertically over the other end, it 

 is plain that the water before it leaves the tube must have acquired 

 the forward velocity of the train as well as the vertical velocity 

 with which it ascends the tube ; and in fact the illustration of the 

 inclined plane pushed beneath the water (p. 49), if properly worked 

 out, shows this very point : e. g. conceive a particle (P) at rest 

 acted on by no forces, and an inclined plane (with an angle a) 

 moving forward with a velocity V to come into contact with it ; an 

 instantaneous action takes place between the plane and the point 

 along the perpendicular to the plane ; and after the action, P will 

 move with a uniform velocity along a line in space coinciding with 

 the position of the perpendicular at the instant of the action. If 

 we further suppose that there is no force of restitution, P, while 

 moving in space along the above-mentioned line, will continue to 

 touch the plane and appear to run up it. Supposing the mass of 

 the plane large in comparison with that of P, the horizontal and 

 vertical components of P's velocity will be V sin 2 a. and V sin « cos et. 

 It is evident from the former expression that, if the plane were 

 steep, the forward horizontal velocity of P would be nearly equal 

 to Y, and would be quite equal to it if the plane were vertical. 

 The velocities would be increased if there were restitution, and the 

 point would be thrown forward from the plane, of course along the 

 aforesaid perpendicular. This is true supposing P to be not acted on 

 by any other force than the momentary action of the plane ; if we 

 suppose P to be under the action of gravity, the above velocities 

 are its horizontal and vertical initial velocities, and the subsequent 

 motion can be easily determined on the usual suppositions. Wow 

 the contrivance for feeding running trains with water differs from 

 the case we have been considering in this — that instead of a mere 

 inclined plane, a tube with a gradually increasing slope is em- 

 ployed ; the effect of this is threefold : in the first place, the increas- 

 ing slope makes the action gradual instead of instantaneous, thereby 

 diminishing the tendency of the instrument to dash the water out 

 of the trough ; in the next place, if the water, when once in the 

 tube, have any tendency to fly forward owing to restitution or any 



