M. Lorenz on the Theory of Light. 



205 



Fig. 4. 



an elliptically- bored gun (see fig. 4), the 



angle P Q represents the angle S, and 



■p 

 we obtain p- by substituting in (31) the 



value of this angle; by putting £ = 90°, 

 we may derive equation (13) directly 

 from (31). 



We have not in this note entered into 

 the question of the absolute pressures 

 existing in the bores of ordnance of 

 various natures, as the subject is too 

 extensive and of too great importance to 

 be disposed of within the limits of a short 

 paper. 



Artillerists acquainted with the subject will be able to form 

 rough approximations to these pressures from the experiments 

 made abroad with smooth-bored guns, with a view to the eluci- 

 dation of this important question. It is much to be regretted 

 that no experiments of the nature referred to have been attempted 

 in England under Government auspices, as they are of a descrip- 

 tion which precludes their being satisfactorily made by private 

 individuals, and as the information to be derived from them 

 would be especially important in the case of rifled cannon, where 

 so many new conditions are introduced into the problem as to 

 render previous investigations of but little value. 



We shall, however, in a future note endeavour to discuss this 

 subject, making use of the data at present at our disposal. 



Elswick Engine Works, 

 June 1863. 



XXIX. On the Theory of Light. By L. Lorenz. 



[Concluded from p. 93.] 

 II. Integration of the Differential Equations : Double Refraction 

 and Chromatic Dispersion. 



IN the differential equations (A) which express the laws of the 

 motion of light in heterogeneous substances, without, however, 

 making any distinct assumption as to the nature of the vibra- 

 tions, there occurs only one function, namely o>, which is directly 

 dependent on the heterogeneity of the medium, and can there- 

 fore be any function whatever of x y y, and z. Such a function, 

 as is well known, can by Fourier's theorem be represented gene- 

 rally by the equation 



^=^2 [i + SCpCOBfi,], 



(1) 



