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Physics. — "On the propagation of Ihjht in a biaxial crystal around 

 a centre of vibration." By H. B. A. Bockwinkel. (Commu- 

 nicated by Prof. H. A. Lokentz). 



(Communicated in the Meeting of January 1906). 



In the electromagnetic theory of light, it is of interest to determine 

 the electromagnetic field in a crystal due to an action, taking place 

 in a certain centre 0. In order to fix the ideas, we shall assume, 

 that in an element of space t at the point there are certain 

 periodic electromotive forces {E. M. F.). There will then be a radiation 

 of energy from in every direction, the amount of which will 

 depend on this direction with respect to that of the E. M. F. 

 and to those of the axes of electric symmetry. Our object is to 

 investigate this dependence, at least for points at a great distance 

 from 0. We might for this purpose use the results of Grünwald ') ; 

 this physicist however takes the equations in the form they assume 

 for a rigid elastic body and does not operate with an E. M. F. as 

 mentioned above; we shall therefore treat the problem independently. 

 Our method will consist in reducing the question to one of plane 

 waves, by using a formula, proved by Prof. Lorentz. In this formula 

 a continuous function of the coordinates is represented by an integral 

 over the solid angles of all cones having their vertices in and 

 filling the whole space. If the E. M. F. is €« then 



r 1 d'iö 



where dn is the element of a line of arbitrary direction within the 

 cone doi and 9B a vector given by 



i> — I e« c^<7, (2) 



the integral being taken over the plane, passing through the point 

 considered, perpendicularly to n. Hence, 5B depends on the coordi- 

 nates, but in such a way as to be constant in every plane perpen- 

 dicular to n. By (1) the original E. M. F. has now been decom- 

 posed into a great number of infinitely small vectors, the effect of 

 which can efisily be calculated, each of them being constant in 

 planes of a certain direction. Thus we determine the field, produced 

 by each of the elements of the integral (1) and then compose all 

 the fields obtained in this way into one resulting field, which. 



1) J. Grünwald. Über die Ausbieitung der Wellenbewegungen in optisch zwei- 

 achsigen elastischen Median, Boltzmann Festschrift (1904), p. 518. 



