422 Drs. Korteweg and de Vries on the 



s 



at the constant pressures of 100, 102, and 104 volts respec- 

 tively consisted of specially good specimens. 



In applying the rule that the economical potential differ- 

 ence is about the one which causes the lamp to produce 0'25 

 candle per watt, it is important, however, to examine 8-candle 

 100-volt Edison-Swan lamps when bought to see whether 

 they are really marked " 100 E.F. 8." For while the result 

 of various purchases of 8-candle 100-volt Edison- Swan lamps 

 during the past three years has always resulted in lamps 

 marked " 100 E.F. 8" being sent us, although the marking 

 on the lamps was never specified by us, a recent batch of 

 lamps that we have received contained among them certain 

 lamps marked " 100 B. 8," which not only differed in the 

 marking but also in the filament being of a simple horse-shoe 

 shape, and not with a loop at the top as in the case of the 

 other lamps. And, on testing these Edison-Swan B lamps, 

 we were surprised to find that with no one of them, when run 

 at 100 volts, did the watts per candle exceed 3*9, and in some 

 cases the watts per candle were as low as 3'01. We have 

 not, however, had these B lamps for a sufficiently long time 

 in our possession to be able to express any opinion about their 

 life-history. 



XLI. On the Change of Form of Long Waves advancing in a 

 Rectangular Canal, and on a New Type of Long Stationary 

 Waves. By Dr. D. J. Korteweg, Professor of Mathematics 

 in the University of Amsterdam, and Dr. Gr. de Veies *. 



Introduction. 



IN such excellent treatises on hydrodynamics as those of 

 Lamb and Basset, we find that even when friction is 

 neglected long waves in a rectangular canal must necessarily 

 change their form as they advance, becoming steeper in front 

 and less steep behind f. Yet since the investigations of 

 de BoussinesqJ, Lord Rayleigh§, and St. Tenant || on the 

 solitary wave, there has been some cause to doubt the truth 

 of this assertion. Indeed, if the reasons adduced were really 

 decisive, it is difficult to see why the solitary wave should 



* Communicated by the Authors. 



t It seems that this opinion was expressed for the first time by Airy, 

 " Tides and Waves," Encyc. Metrop. 1845. 

 X Comptes Rendus, 1871, vol. lxii. 

 § Phil. Mag. 1876, 5th series, vol. i. p. 257. 

 || Comptes Rendus, 1885, vol. ci. 



