248 Proceedings and List of Papers read. 



the oscillator. A fourth wave dealt with by Hertz, namely, the wave 

 of magnetic induction, does not, as he supposes, start with zero phase 

 from the origin, but with a finite phase. The wave in the equatorial 

 plane, largely relied upon by Hertz for his interference experiments 

 " of the first kind," is a compound of the waves of transverse and axial 

 electric force, and has a much more complex series of velocity changes 

 than Hertz appears to have realised. 



(iv) The existence of the two electric force waves and the singular 

 points or surfaces for the wave motion in the neighbourhood of the 

 oscillator very possibly throw light on the difficulties which arise in 

 Hertz's experiments. It would seem that such experiments should be 

 made at distances greater than 6 to 7 (A/27r) from the centre of the 

 oscillator, or, roughly, about a wave-length from the oscillator. In 

 Hertz's case this amounts to about 10 metres a distance at which 

 Hertz rather terminated than started his interference experiments. Only 

 at such a distance are the phase curves sensibly linear. 



The authors are not unaware of the physical difficulties of experi- 

 ment at great distances, and wish, therefore, to emphasise again the 

 fact that they are dealing with a theoretical oscillator. It is, however, 

 this type for which Hertz himself endeavoured to provide a mathe- 

 matical investigation, and it is that investigation which, in the first 

 instance, they have attempted to expand and modify. 



January 26, 1899. 

 The LORD LISTER, F.R.C.S., D.C.L., President, in the Chair. 



A List of the Presents received was laid on the table, and thanks 

 ordered for them. 



The Right Hon. G. J. Shaw-Lefevre, a member of Her Majesty's 

 Most Honourable Privy Council, was balloted for and elected a Fellow 

 of the Society. 



The following Papers were read : 



I. " Contributions to the Theory of Simultaneous Partial Differential 

 Equations." By Dr. A. C. DIXON. Communicated by Pro- 

 fessor G. J. ALLMAN, F.R.S. 



II. " On the Structure and Affinities of Fossil Plants from the Palaeo- 

 zoic Rocks. III. On Medullosa anglica, a new Representative 

 of the Cycadofilices." By Dr. D. H. SCOTT, F.R.S. 



