Revieius and Notices of Books. 



119 



Then, again, in works of a somewhat more ambitions character, 

 in which the subject is treated analytically, the mode by which 

 you are led to a result is very much the same as that by which 

 the railway traveller who journeys by night arrives at his des- 

 tination — the process is not invigorating, and there is no appre- 

 ciation of the beauties of the way. So when you have once 

 formed your differential equation, and abandoned yourself to the 

 labour of solving it, you have quite lost sight of the physics and 

 the geometry of the problem. 



In the present pamphlet, which we are content to view only as 

 an instalment, the authors have, we think very successfully, in- 

 troduced much of the beauty of the geometrical method with very 

 little of its cumbrousness. They have also availed themselves to 

 the fullest extent of that great discovery of modern times — the 

 conservation of energy ; and we shall afterwards adduce an ex- 

 ample of their happy employment of this principle. We must 

 add to this a philosophical arrangement and a unity of concep- 

 tion in order to characterise the book. So novel are many of 

 its solutions, that our first emotion is that of surprise, as we re- 

 cognise some very old friend in his new dress ; while our second 

 is altogether one of pleasure from his improved appearance. 



We now quote a few lines from the commencement of the 

 volume : — - 



" Dynamics is the science which investigates the action of force. 

 Force is recognised as acting in two ways, — Isi, So as to compel 

 rest or to prevent change of motion ; and, 2(i, So as to produce or 

 to change motion. Dynamics, therefore, is divided into two parts 

 — Statics and Kinetics. 



In Kinetics it is not mere motion which is investigated, but the 

 relation of force to motion. The circumstances of mere motion, 

 considered without reference to the bodies moved or to the forces 

 producing the motion, or to the forces called into action by the 

 motion, constitute the subject of a branch of pure mathematics, 

 which is called ' Kinematics.' " 



The first part of the pamphlet is therefore devoted to Kine- 

 matics. Here, after defining velocity, it is shown, that if two 

 velocities be represented by the sides of a parallelogram, their 

 resultant is represented by its diagonal. Acceleration, in its 

 most general sense, is defined as the ''^ rate of change of velocity, 

 whether this change take 'place in the direction of motion or not 

 also, " the moment of a velocity or a force about any point is the 

 rectangle under its magnitude, and the perpendicular from the 

 point upon its direction." It is then shown, that the moment 

 of the resultant velocity of a particle about any point in the plane 

 of the components is equal to the algebraic sum of the moments 

 of the components. 



