June i6, 1892] 



NATURE 



U7 



scribed ; but it should be pointed out that the pen- 

 dulum in which the gun itself is mounted gives very 

 untrustworthy records, as the effect of the blast of the 

 powder and of the air dragged along with it is so very 

 great. The Ballistic Pendulum is still useful for deter- 

 mining the velocity of small-arm bullets, but for artillery 

 purposes the electric chronograph has completely sup- 

 planted it. 



Chapter IV. discusses Motion in Two Dimensions, and 

 is perhaps the most generally important and interesting 

 chapter in the book. A complete dynamical terminology 

 is still a desideratum, and many new words • must be 

 coined ; for, as De Morgan remarks, " We cannot wait 

 for words, because Cicero did not know the Differen- 

 tial Calculus (or Dynamics)." At the same time it is 

 a pity that the old word Vis Viva, meaning Mz/'^, was 

 not allowed to drop, to be replaced by Kinetic Energy, 

 for \'h\v-. Vis mortua is forgotten as the name for Work, 

 and 7'is viva, as the other manifestation of energy, should 

 go too. 



The dot notation of Fluxions has been introduced in 

 places : this, though easy to write, is difficult to print, and 

 is inconvenient sometimes with tall letters, while others, 

 like i and 7, are already in their " dotage." 



Dr. Routh would, in our opinion, make the working of 

 the illustrative examples more clear, if he always followed 

 the fundamental principle of taking moments about the 

 centre of gravity, as if it was a fixed point : very few 

 students can be trusted to apply the principle to moments 

 about any other moving point, and the equations of relative 

 motion on p. 178 are better kept out of sight of all but 

 a select few. 



Dr. Besant's treatment of questions on Initial Motion 

 is in our opinion simpler of application and quite as 

 rigorous as that given in § 199. 



A very good collection of illustrative examples com- 

 pletes this chapter, but we miss the extension of the 

 problem of the motion of a cylinder rolling down an 

 incline to the case of a wheeled carriage or of a railway 

 train, when the rotary inertia of the wheels is taken into 

 account, including the determination of the proper 

 position of the coupling chains and buffers ; also the 

 investigation of the stresses in the interior of a swinging 

 body like a ship, not only in causing cargo to shift, but 

 also in its physiological bearing on sea-sickness. An 

 ordinary swing is useless as an antidote to sea-sick- 

 ness, as the seat is close to the centre of oscillation. To 

 feel the disturbing effect we must mount up above the axis 

 of revolution ; and to the deck and up the mast of a ship. 



As interesting applications, we may mention the dyna- 

 mics of billiards, §§ 179-98, and of the quintain in § 178. 



After Chapter IV. the author launches off into dyna- 

 mics in space, and now the difficulty of the subject is 

 more than doubled. 



Chapter VII., on Energy (or Vis Viva, as Dr. Routh 

 still prefers to call it), precedes in importance and idea 

 the Chapter VI., on Momentum, and might well change 

 place. The idea of energy as ^Wv'/g very soon received 

 a name for its unit in the /ooi-pound, but the correspond- 

 ing name for the momentum, Wvjg, of second-pound is 

 as yet hardly known. 



In this chapter the Principles of Dynamical Similitude 

 are discussed. In Geometry the Principle of Similitude 

 NO. I 181, VOL. 46] 



asserts that a theorem is true whatever the scale on which 

 it is drawn ; but in Dynamics the principle is much more 

 complicated, and great care is required in arguing 

 from the performance of a model or of a machine to one 

 to be constructed to a larger scale. The subject is one 

 of great importance at the present time in the discussion 

 of the design of steamers intended to reduce the time of 

 passage across the Atlantic to something under six days ; 

 and the statement of the laws to be applied as affecting 

 steamers, first clearly laid down by Mr. Froude, might 

 well find explanation and illustration at this point. 



The impact of two rough elastic ellipsoids is treated in 

 §§ 315, &:c., by a mathematical tour de force ; but the 

 expression perfectly rough is never met with outside a 

 Cambridge mathematical treatise. What would be the 

 state of things, for instance, between two bodies in con- 

 tact, one perfectly rough and the oihtx perfectly smooth f 

 When we wish to produce this so-called perfect rough- 

 ness between two bodies, we cut teeth on them, to engage 

 together ; and in railway travelling the perfect smooth- 

 ness of the road due to the employment of wheels must 

 be capable of being turned into roughness by the appli- 

 cation of the breaks : the continuous breaks now fitted 

 to express trains have enabled a higher average speed to 

 be maintained. 



The General Equations of Motion of Lagrange and 

 Hamilton, discussed in Chapter VIII., are not to be 

 employed by any but very advanced students : the for- 

 mation of these equations and the conversion of one 

 form into the other constituting difficult and refined 

 applications of the Change of the Variables. 



In the case where some of the co-ordinates are absent, 

 this part of the subject has received valuable develop- 

 ment from Dr. Routh, by means of a principle now 

 called the Ignoration of Co-ordinates. 



The volume concludes with an investigation of the 

 Small Oscillations of a System, important as a Stability 

 Test ; in such problems the author expresses the result 

 very concisely by means of the length of the simple 

 equivalent pendulum which synchronizes with the oscil- 

 lations. An interesting problem to discuss is the theory 

 of Mr. Yarrow's Vibrometer, employed for measuring the 

 vertical vibrations of his torpedo-boats : a platform 

 suspended by springs is found to preserve a constant 

 level, if the free period of the vertical oscillations of the 

 platform is incommensurable with the period of the 

 vibrations of the boat. 



It is difficult to know where to stop in writing of 

 treatises such as these two of Dr. Routh, so full of 

 detail and interest ; and the two treatises together would 

 provide nearly a year's work for an industrious student, 

 who would thereby derive a thoroughly sound and com- 

 plete knowledge of the subjects. 



A. G. Greenhill. 



COLLECTIONS FROM THE ANDES. 

 Supplementary Appendix to Travels amongst the Great 

 Andes of the Equator. By Edward Whymper. (London: 

 John Murray, 1891.) 



THOUGH many travellers in new or httle-known re- 

 gions, who are not naturalists, have been in the 

 habit of collecting to some extent the more remarkable 



