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conception of continuous change emphasised by certain modern philosophers. 

 After curves of velocity for motion in two dimensions, including the hodograph 

 and accelerations, have been dealt with, a number of examples of rectilinear motion 

 are considered, one being a neat investigation of the motion of the crosshead of a 

 steam engine relative to the fixed frame and to the crank pin. A very interesting 

 and important fundamental theorem relating to moving axes is then enunciated and 

 proved ; this is applied afterwards to the solution of gyrostatic problems of interest 

 to the scientist and to the engineer. The remainder of this chapter deals with 

 more difficult acceleration problems, three-dimensional motion and harmonic 

 motion. In Chapter II. dynamical principles are discussed, the laws of motion 

 and work and activity being fully considered. This chapter may be specially 

 commended to all serious students and to teachers of dynamics, as the discussion 

 of the laws of motion is suggestive and illuminative and the results obtained both 

 for bodies of constant and variable mass are of great importance. In the next 

 chapter the motion of a particle in a resisting medium is considered, a number 

 of important examples being solved. James Bernouilli's solution of the time 

 of quickest descent in a given field of force is reproduced and is followed by 

 a general discussion of brachistochrones and the use of the calculus of variations 

 in their solution. The use of the term "conservative forces" without definition is 

 hardly fair to readers ; later in the volume the authors seem to recognise this, 

 as the term is defined in Chapter X. Chapter IV. deals almost entirely with 

 astronomical problems, the free motion of a particle under a force directed to 

 a fixed point being fully discussed. A short chapter on the motion of rigid 

 bodies, in which a number of important theorems are given, is followed by an 

 interesting chapter on the application of dynamical principles. On account of its 

 suggestiveness as well as for the importance of the results deduced, the first part 

 of this chapter will well repay perusal by engineers directly interested in traction : 

 we know of no other English work in which the dynamics of the subject is so well 

 treated. On p. 351, on which the problem of an engine running round a curve 

 is considered, there is a slight error, the 2b in the figure corresponding to b in the 

 text. The gyrostatic effect of the wheels of the locomotive as the engine runs 

 round the curve is dealt with later, though it might well have been considered 

 here as a direct application of the important principle mentioned above. The 

 possibility of oscillations causing an engine to leave the track at speeds below the 

 so-called critical speed is considered but the important effect of the unbalanced 

 masses on the crank shaft is not dealt with ; an application of the principles of the 

 previous chapter will, however, enable the reader to obtain the magnitude of 

 the overturning couple due to these masses. In this chapter, the compound 

 pendulum and forced vibrations are dealt with and consideration is given to the 

 pile driver and ballistics. After a short chapter on the rotation of rigid bodies, 

 tops and gyrostats are comprehensively treated ; the interest and importance of 

 this chapter will be obvious when it is said that in addition to the analogy 

 of motion of an electron in a magnetic field to the motion of a gyroscope being 

 considered, astronomical precession, the Schlick gyrostatic controller of rolling 

 ships, the barygyroscope for demonstrating the earth's rotations, the Brennan 

 mono-rail, the gyrostatic action of revolving masses in steamers and the 

 gyrostatic couples on locomotives and carriages when running round curves 

 or running over a track with changing gradient are all considered. In Chapter X. 

 general dynamical principles are dealt with, Lagrange's and Appell's equations 

 and Hamilton's transformation of the equations of Lagrange being elegantly 

 treated. A number of applications of these equations is also given. The work 



