Notices respecting New Boohs. 393 



and there will be the corresponding subsidence in the ampli- 

 tudes of the two sets of waves travelling outwards in all 

 directions at great distances from the origin, when, according 

 to the propagational velocities, u, v, the effects of the stoppage 

 of the maintaining force reach any particular distance. 



It is quite an interesting mathematical problem, suggested 

 at the end of § 44, to fully determine the motion in all future 

 time, when m is left with no applied force, alter any given 

 initial conditions, with any value, large or small, of m/Q. 



§ 46. Returning now to the maintenance of vibrations at 

 the rate of lOOGi periods per second ; and u, v for granite ; 

 and q = b cm., all as in § 43 : see (98) and remark that, to 

 make E/rto very large, s must be a very small fractional 

 numeric ; and this makes m/Q=s. To take a vibrator not 

 differing greatly in result from the violin-string suggested in 

 the addition of March (5, referred to in §33 above, let ?n be 

 a little ball of granite of \ cm. diameter. This makes 

 m = Q/8000, and therefore (§ 40) s = 1/8000. Hence by 

 (98), E/tu>= 1872001, from which, with what we know of 

 wave-motion, we infer that if m be projected with any given 

 velocity irom its position of equilibrium, it will, for ever after, 

 vibrate, with amplitude diminishing according to tie formula 



C € 3^sin— . . . . (101). 



T 



Thus during 3,754,002 periods the range of m will be 

 reduced in the ratio of e to 1 (say approximately 2f to 1), by 

 giving away its energy to be transmitted outwards by the two 

 species of waves, of which [according to J of (97)] the equi- 

 voluminal takes twelve times as much as the irrotational. 



XLI. Notices respecting New Books. 



Unites Electrignes absohtes. Lemons professees a la Sorbonne par 

 G. Lifpmann. (Paris, Carre & Naud, 1899. 8vo, pp. ii + 240.) 



r PHE course of lectures delivered in 1884-5, and now published 

 J- under the above title, treats of electric and magnetic phenomena 

 from the point of view of the measurement of the quantities that 

 occur in the theories of such phenomena. The author in general 

 assumes the phenomenon to be known, gives a brief sketch of the 

 theory connected with it, and pays special attention to the physical 

 nature of the quantities involved, discussing the dimensions of 

 their units in electrostatic and electromagnetic measure, describing 

 the kind of apparatus that can be employed in measuring them, 

 and pointing out the difficulties incident to various experimental 

 processes. The course is in two parts, the first part dealing with 



