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aCIENCK 



[N. S. Vol. XI. No. 276. 



surpassing the Nobert plate in brilliance also 

 , succeeded. Since to resolve the D lines the 

 distance between the rulings must be true to 

 1/1000, this performance seems incredible. Yet 

 Rayleigh anticipates no limit to his method up 

 to 10,000 lines to the inch. Copies of similar 

 gratings made in accordance with Rayleigh's 

 directions are found in most of our laboratories. 

 They have not held their own owing to the 

 enormous stride forward in diffraction spectro- 

 scopy due to the invention of Rowland's con- 

 cave grating. Connected with these papers is 

 one on the diffraction of object glasses in tel- 

 escopes, in which the advantage of a central 

 stop to out off superfluous light without destroy- 

 ing the definition is succinctly laid down. 



Of Lord Rayleigh's highly important contribu- 

 tions to mathematical literature made at about 

 this time, bare mention only is possible here. 

 A paper on some general theorems relating to 

 vibrations deals with great breadth of method 

 with the reciprocal character of forces and mo- 

 tions of any two types. To quote an illustra- 

 tive example : If A and B are two points of a 

 stretched string, a periodic transverse force at 

 A produces the same vibration at B as would 

 have ensued at A for a force acting at B. 

 Another paper treats of the numerical calcula- 

 tion of fluctuating functions (Bessel functions, 

 for instance, though the method has broader 

 scope) when the usual espansions in series fail. 

 Again the reciprocal properties of systems 

 capable of vibrating about a position of equi- 

 librium, is accentuated in a further paper put 

 in form of a statical theorem. Of these power- 

 ful theorems (together with a parallel theorem 

 of Helmholtz) Rayleigh frequently makes effec- 

 tive use, and reference to them occurs in other 

 parts of the volume, either in relation to sound 

 or to light. Finally, the proof of Thomson's 

 theorem, that if a material system start from 

 rest under the action of given impulses, the 

 energy of the actual motion exceeds that of 

 any other which the system might have been 

 guided to take under the operation of con- 

 straints, etc. , is recast in such a way as to sug- 

 gest important corollaries. 



Two papers on thermodynamics now appear. 



It is Rayleigh's idea to utilize the fall of tem- 

 perature between the furnace and the boiler as 



well as that between boiler and condenser by 

 supplementing the steam engine with an auxil- 

 iary oil engine, and the development leads to 

 a discussion of the doctrine of dissipation. 

 Again the case, where work may be gained by 

 mixing gases, as for instance when hydrogen 

 diffuses into air through a porous plug, is sub- 

 jected to computation, by finding the work 

 needed to separate a mixture. The line of 

 reasoning adopted by Lord Rayleigh in this 

 paper reminds one of the fundamental research 

 of van't Hoflf, though it breaks off with the 

 isolated case under discussion. The interesting 

 result is formulated that relatively more work 

 is needed when the ingredient to be separated 

 is present in small quantitJ^ 



At this point we come upon a series of dis- 

 tinctively hydrodynamic researches, beginning 

 with a paper on gravitational waves. The 

 case of the long wave in shallow water was 

 solved by Lagrange, who showed that its ve- 

 locity is identical with that of a heavy body 

 falling half the depth of the canal. If the 

 w'ater itself moves with an opposed velocity, 

 the wave form is of the steady type often ob- 

 served in gutters convej'ing water. After en- 

 larging the theory of long waves, Rayleigh ap- 

 plies it to find the efiect on a stream of a con- 

 traction or a widening of the channel, to the 

 case of the solitary wave (for which he finds a 

 theoretical explanation agreeing with Scott 

 Russel's observations. The solitary wave when 

 positive, i. e., an elevation, has considerable 

 permanence. The negative wave on the con- 

 trary soon breaks up), to periodic water waves 

 and to the oscillations of water in a cylindrical 

 vessel. 



This research is followed shortly after by an 

 investigation of the resistance of fluids. Helm- 

 holtz had previously pointed out that finite 

 slipping was left out of account on ordinary 

 hydrodynamics. Rayleigh is induced to re- 

 open the subject with the ulterior object of 

 formulating the resistance encountered by a 

 solid body floating in a stream. In the case 

 of a plate it appears that the resistance to 

 broadwise motion can be increased enormously 

 by the superposition of an edgewise motion, 

 a result of great value in aerial navigation. 

 It recalls the striking results obtained by 



