152 TRANSACTIONS OF SECTION A. 



2. The Diffraction of Electric Waves. 

 By G. N." Watson, Sc.T)., F.R.S. 



The theory of the fundamental mathematical problem presented by long- 

 distance wireless telegraphy has been investigated by Poincare, Nicholson, 

 Macdonald, Love, and by some of Sommerfeld's pupils, on the hypothesis that 

 the earth consists of a sphere of high conductivity surrounded by dielectric. 

 The results obtained are not obviously consistent, and thev do not agree -with 

 experimental results. I have recently obtained a general formula whereby the 

 theoretical results can be reconciled . and this formula shows that the magnetic 

 force at angular distance and from the transmitter is roughly proportional to 

 exp( — 23-94 e/yx), where \ is the wave-length in kilometres. The experimental 

 result obtained bv Austin is exp( — 9-6 9/a/X). In order to obtain this result 

 (which is obviously inconsistent with the result of the diffraction theory) by 

 mathematical reasoning, I have investigated by my method the Heaviside- 

 Ekicles hypothesis that the upper regions of the atmosphere act as a conductor, 

 and Austin's formula is exactly obtained if 



AV =z 1-67 X 10", 



where h is the height in kilometres of the conducting layer above the surface 

 of the earth and o- is the conductivity of the layer in rational units. If 

 A = 100, this formula gives the layer a conductivity of about 3-5 times the con- 

 ductivity of fresh water. The mathematical investigations are given in detaii 

 in tvro papers, Pror. Tioyal Boc. 95a, and also in a paper by Dr. van der Pol 

 in the Phil. Mag., September 1919. 



In the course of discussion of the above paper. Dr. B. van der Pol said : — 



I consider that the mathematical work of Macdonald. Nicholson, and Watson 

 does not leave the slightest doubt that the propagation round the earth of wire- 

 less waves cannot be explained by means of pure diffraction only. 



As expounded by Prof. Watson, numerical agreement with experiments can 

 be obtained when a concentric spherical shell ha^^ng a certain conductivity is 

 supposed to surround the globe. This shell was taken for mathematical reasons 

 to have a sharp inner boundary. Such a boundary can hardly be expected to 

 exist in the upper atmosphere, and it is likely that in a transition resjion con- 

 siderable amounts of energy will be dissipated. When, however, regard is taken 

 of the equation of motion of free ions in an alternating field, as indicated by 

 Professor Eccles several vears ago, it appears that the medium has not only a 

 finite conductivity, but also an apparent diminution of the dielectric constant e 

 must occur. 



In some experiments carried out at the Cavendish Laboratoi"^', Cambridge, 

 I have used as ionised medium the negative glow of a p-low- discharge, and 

 waves were sent through it. Results were obtained confirming- thp above view. 

 As this diminution of e with height causes the wnvefront to fall over in the 

 direction of propagation, and is therefore favourable to wireless tr.nnsmission, 

 it is not unlikely that, when this increase of phase velocity -with height is taken 

 into account, the propagation of waves round the earth can be explained with 

 the assumption of a gradual variation with height of conductivit}' and apparent 

 dielectric constant. 



3. 0)7 a possible Theory of Vision. By Sir Oliver Lodge, F.R.S.i 



A resonance view of the action of the retina has long been in contemplation.! 

 The present writer pointed out in Nature for March 1890 that the rods audi 

 cones were of reasonably right dimensions to respond, like Hertz resonators,! 

 to transverse vibrations falling on their ends with the frequency of luminous^ 

 waves. (See also Modern Views nf Elecfririty , § 157A and fig. 60.) 



But this gave no indication of how the nerves were thereby stimulated. Thel 

 subsequent discoveries of excited radioactivity, and of the astronomical structure! 

 of an atom, give a hope of a more detailed theory. 



