Colours diffusely reflected from some Collodion Films. 423 



then 

 _/c(afi" + b\"+p"— abv") + 2{aq+bp + 8-abr)(\'fi' + v'p') 

 «(a/j/ + b\' + p' — abv') 



+ F(a,r) + F*(6,r), 

 _ fc(a fju a " + b \ " + po" — a b v ") — 2(a q -f b p + s — a b r)(X / fi i} ' -f Vo'po) 

 /c(a fM Q ' + 6 X ' -f p ' — a b Q v ') 



+ F (fl , t )+F *(6 , t ). 



Let us regard a and 6 as the circular coordinates of a point 

 in a plane then when ^, ^ , t, r are given constants, the above 

 equations represent two circular curves which generally inter- 

 sect in a finite number of points and with each of these points 

 we can associate just one set of values of x, y, z, and t. This 

 means that the line of force (%, t) intersects the line of force 

 (%o> T o) a finite number of times. These lines of force will 

 thus generally cut through one another, but if the two 

 circular curves touch at all their common points the lines of 

 force will meet and rebound. 



It may happen that the two circular curves are the same 

 or have a common part. In this case there is permanent 

 incidence between the two lines of force. The number of 

 relations which must be satisfied by %, % , r, and r in order 

 that the two curves may have a common part, may be either 

 one, two, three, or four. The first three cases may be dis- 

 cussed geometrically in the same way as before ; in the 

 fourth case there is permanent incidence between only a 

 finite number of lines of force of the two fields. If such 

 cases exist in nature, it is possible that the moving points of 

 incidence are occupied by electric charges and that when 

 the fields of a large number of moving charges are super 

 posed each charge is a point of incidence of a number of 

 lines of electric force. 



XXXIX. On the Colours diffusely reflected from some Col- 

 lodion Films spread on Metal Surfaces. By Lord Rayleigh, 

 O.M., F.R.S.-\ 



IT is known that " when a thin transparent film is backed 

 by a perfect reflector, no colours should be visible, 

 all the light being ultimately reflected, whatever the wave- 

 length may be. The experiment may be tried with a thin 

 layer of gelatine on a polished silver plate " ±. An apparent 

 exception has been described by R. W. Wood § : "A thin 



t Communicated by the Author. 



I Wave Theory, Enc. Brit. 1888 ; Scientific Papers, vol. iii. p. 67. 



§ ' Physical Optics,' Macmillan, 1914, p. 172. 



