Bending of Electric Waves round a Large Sphere. 755 



case the dry film should be well exposed to light before 

 washing. Ready-made varnishes also answer well provided 

 they are capable of withstanding the action of water, at least 

 for a time. I have used amber in chloroform, a " crystal" 

 (benzole) varnish such as is, or was, used by photographers, 

 and bitumen dissolved in benzole. The last is soon disinte- 

 grated under water, but the crystal varnish gives very good 

 films. The varnish as sold may probably require dilution in 

 order that the film may be thin enough. 



Another varnish which gives interesting results is celluloid 

 in pear-oil. All these films show little in air, but display 

 beautiful colours in water when the reflexion from the back 

 of the glass is got rid of as already described. The advantage 

 from the water depends, of course, upon its mitigating the 

 inequality of the reflexion from the two sides of the film by 

 diminishing the front reflexion. A similar result may be 

 arrived at by another road if we can increase the back re- 

 flexion, with the further advantage of enhanced illumination. 

 For this purpose we may use silvering. A glass is coated 

 with a very thin silver film and then with celluloid varnish 

 of suitable consistency Magnificent colours are then seen 

 without the aid of water, and the only difficulty is to hit off 

 the right thickness for the silver. Other methods of ob- 

 taining similar displavs are described in Wood's ' Phvsical 

 Optics ' (MacMillan, 1905, p. 142). 



./ 



LXXVIL On the Bending of Electric Waves round a Large 

 Sphere.— V. By J. W. Nicholson, M. A., B.Sc* 



Points near the axis in the region of hrightness. 



WE can now show that the second approximation obtained 

 in the preceding section f for points in the region of 

 brightness does not fail near the axis, and, in fact, we can 

 derive the solution for this entire region without the use of 

 an approximate formula for the zonal harmonic. A brief 

 account of this investigation is now given, as most of the 

 necessary analysis has already appeared in the section imme- 

 diately preceding, the main difference being dependent on 

 the mode of treatment of P n (/^). If the accurate Mehler 

 Dirichlet integral is used for this function, the magnetic 



* Communicated by the Author, 

 t Phil. Mag. Mar, 191], p. 281. 



