On Discontinuous Wave-Motion. 203 



The values of n for the paraffins calculated from the 

 formula, using observed calorific values and vapour densities, 

 are very close to the known numbers, and those found for 

 the fuel mixtures can probably be accepted to the s;ime 

 degree of certainty. It is noticeable that the ratio of the 

 weight of air for complete combustion to that of the vapour 

 burnt is highest in methane and falls rapidly to a normal 

 value in butane. The mean ratio for all the substances is 

 15*5 lb. of air to one of fuel, and the variations are small. 

 The mean number of oxygen atoms for complete combustion 

 of the mixtures is 20*7, corresponding to a mixture of almost 

 equal proportions of hexane and heptane if these alone are 

 present. 



6. In the same way when the calorific value of any liquid 

 or gaseous fuel is unknown, it can be determined by fin ding- 

 hy explosion the volume of air required to burn completely 

 a measured volume of the vapour of known density. If, 

 for example, 50 volumes of air are required for one of 

 vapour, and the measured vapour density is 3*2, the per- 

 centage of gas is 1*96, w = 20'4, and the heat of combustion 



20-4x10* Q0 lk q£ Qr H = ll00 



6'0'lb x d ' l 



large calories per gram molecule. 



XVI . On Discontinuous Wave-Motion : Part II. 

 By C. V. Raman, M.A., and Ashutosh Dey*. 



[Plate III.] 



IN an important paper on the theory of discontinuous 

 wave-propagation f , Harnack has given an elegant 

 general formula expressing the mode of vibration of a 

 string whose configuration is completely determined by 

 a finite number of discontinuous charges of velocity travel- 

 ling over it. As an illustration of his result, Harnack has dis- 

 cussed, in some detail, the cases in which the form of vibration 

 is determined by one and by two such changes of velocity 

 respectively. The analysis indicates that the case of a 

 single discontinuity is identical with that of the principal 

 mode of vibration of a bowed string, and in a previous 

 communication from this laboratory J it has been shown 



* Communicated by the Authors. 



t A. Harnack, Mathematische Annalen, vol. xxix. p. 486. 

 t 0. V. Raman, M.A., and S. Appaswamaij^ar, " On Discontinuous 

 Wave-Motion." Phil. Mao-. Jan. 1916. 



