646 Mr. J. S. Dow on a Form of 



Similarly, the illumination o£ the surface facing B is 



2 „ 5- nence if Ii = l2 the surfaces appear equally illu- 

 minated and we obtain photometric balance, with the wedge 

 in its symmetrical position. 



Suppose now that Ij is greater that I 2 , and that it is 

 therefore necessary to rotate the wedge through an angle 0, 

 in a clockwise direction, in order that the illuminated surfaces 

 may appear equally bright. 



The illumination of the surface presented to A is now 



— = , and the illumination of the surface presented 



, -p . I 2 cos (u — 6) 

 to B is — ) h '- . 



Therefore I x __ cos (a— 6) 



I 2 "" cos (a + 6)' 



The ratio ~ corresponding to each value of 6 is therefore 



2 

 known. In this case the angle a was made 45° for, by so 



doing, the maximum angular range of photometrical reading 



is obtained. 



A lever, rigidly attached to the wedge and utilized by the 



observer to rotate it, also served as a pointer indicating the 



value of 6 and the corresponding ratio ~ — — , r — -Jr , on 

 a scale attached to the instrument. ^ cos ^ 4o + ^ 



This arrangement is shown in h>. 1. 



The scale is also diagrammatically exhibited in fig. 3. 

 The most serviceable portion of this scale lies in the 

 neighbourhood of 2 to 5'0. Outside this range the values 



of - — \ — -. change too rapidly with increasing values 



of 0, for satisfactory readings. At the extreme ends of the 

 scale, too, the rays necessarily strike one of the photometric 

 surfaces very obliquely, and therefore emphasize any in- 

 equalities or roughness in texture of the surface and reduce 

 the sensibility of the instrument. 



At present fine plaster of paris has been used by the author 

 to secure white matt surfaces. Under these conditions, the 

 theoretical readings on the scale deduced from the cosine law 

 agreed very closely with those obtained experimentally and 

 assuming an inverse square law. 



Between the limits 0*2 to 5 the agreement was within 



3 per cent., and probably the substitution of perfectly ground 

 photometric surfaces for those prepared by hand would result 

 in still closer agreement. 



