506 Prof. J. Perry and Mr. H. F. Hunt on the 



the margins come in contact with one another and thus cause 

 a diminution of the total resistance of the grating. Especially 

 the fact that the spacing of the strips should have so large an 

 influence as to reduce the effect almost to nothing seems to 

 me to favour the ahove supposition. Also the fact that the 

 change of resistance depends upon the orientation of the strips 

 seems to point in the same direction. Still another fact which 

 is equally important from the above point of view is that 

 the resistance of the tinfoil grating once diminished by an 

 exposure to the action of electric waves can he restored nearly 

 to the original value by tapping the grating. It may be 

 pointed out that Prof. Minchin's experiment * on the action 

 of electromagnetic radiation on films containing metallic 

 powders may stand in close connexion with the present 

 subject. 



XLVII. The Development of Arbitrary Functions. 

 By Prof. John Perry and Mr. H. F. HuNTf. 



STUDENTS at the Finsbury Technical College have for 

 some years carried out the Fourier development idea of 

 the late Professor Clifford by practical Geometrical methods. 

 The curve which graphically represents the function is sup- 

 posed to be wrapped round a circular cylinder, and the areas 

 of its projections upon two diametral planes enable the coeffi- 

 cients to be found. In ' The Electrician ' of June 28th, 1895, 

 one of us gave detailed instructions for carrying out the 

 process. We do not know of any method of development in a 

 Fourier series which can compare with this in either rapidity 

 or accuracy. 



In the discussion of Prof. Henrici's paper, April 13th, 1894, 

 one of us described a graphical method of developing any 

 arbitrary function in a series of other normal forms than sines 

 and cosines, such as Bessels or Zonal Spherical Harmonics. 

 It consisted in wrapping the curve which represents the 

 function round a specially shaped cylinder, not circular, and 

 projecting it upon a certain plane. One of us has wasted 

 many months in finding with great exactness a sufficient 

 number of coordinates of the trace of the cylinder suitable 

 for a Zeroth Bessel development. The labour was unneces- 

 sary because the coordinate most troublesome to calculate is 

 not really needed : that is, the actual shape of the cylinder is 



* Phil. Mag. [5] xxxvii. p. 90 (1894). 



t Communicated by the Physical Society: read October 25, 1895. 



