224 Prof. D. N. Mallik on the 



ends of the string. It is not suggested that the shape of the 

 pole-pieces may be calculated, but it seems as if the result 

 may be obtained empirically with sufficient approximation to 

 reduce to an imperceptible amount the undesired harmonics. 

 The field should then be used at the same field excitation at 

 which the measurements were taken because a change in the 

 exciting current will probably change the distribution. The 

 total magnetic flux may be reduced a little but the tapering 

 will tend to increase the intensity near the centre above the 

 value it had for a uniform field, and diminish it near the ends, 

 that is, to redistribute rather than greatly reduce the total 

 field, and consequently the sensitivity would not be reduced 

 as much as might be expected. 



When there is inductance in the circuit of the galvano- 

 meter the differential equation (21) may be used, but its 

 general solution involves the solution of a cubic equation. 

 The solution is feasible in certain particular cases and it may 

 be serviceable for some kinds of work with the galvanometer. 

 If an harmonic current is assumed the permanent periodic 

 portion is readily found ; and this applies to the study of 

 sounds when there is an induction-coil in circuit. 



It is hoped that on a future occasion some records taken 

 with the galvanometer may be given to compare the recorded 

 and calculated curves, and to give numerical values of the 

 constants. 



XXVI. Dynamical Theory of Diffraction. 

 By Prof. D. N. Mallik, B.A., Sc.D., F.R.S.E.* 



1 . T F T is the kinetic energy of a strained elastic medium 

 A of density <r, having displacements £, ??, f at a point 

 #, y* #, then 



2T = JerCf + # + $)fadydg. . . . (1) 



Again, if W = the potential energy of deformation, then, 

 on MacCullaugh's theory, as well as Lord Kelvin's, 



SW = S$2n(<o x 2 + <o ]/ 2 + co z 2 )dxdydz, , . . (2) 



where co x , &c. are molecular rotations, and 8 the operator of 

 the calculus of variation (n being the rigidity). 



On the other hand, the electromagnetic energy in a 



* Communicated by the Author. Paper read before the First Indian 

 Science Congress, Calcutta. 



