162 Dr Searle, Experiments with a prism of small angle 
and for the refraction at R 
Dy= (#1) (Bi — 0) + Au (w—D Gta) oA) 
The whole deviation, D, is the sum of D, and D, and hence 
D=(p—l)itdee (w—1)i(e + 129? 
=(w— em app (uw +1) @ +127). .... 22... (8) 
The term involving 7? shows how lack of symmetry increases the 
deviation. When both 7 and 7 are small, we may write* 
D2G2)t eee (9) 
which is the formula we shall use in the experiment. 
ae 
The prism is placed with its edge vertical in a tank (Fig. 8) | 
with parallel glass sides containing a liquid of refractive index py. 
If the sides of the tank are plates of plane-parallel glass, they will | 
not affect the deviation, and we may treat the system as if it were 
a glass prism in a block of water. We then have three prisms, 
viz. a glass prism of angle 7 and two liquid prisms whose angles 
| 
are 8 and y (Fig. 8), the sum of 8 and y being 2, 8 and y bemg — 
counted positive when the refracting angles of these prisms point 
in the opposite direction to that of the glass prism. Ifa ray now 
oa 
Fig. 8. 
passes through the system, falling nearly normally upon the 
surface of the liquid, it will pass nearly symmetrically through — 
each of the prisms and the formula (9) may be applied to each 
prism. If D, be the resultant deviation, and if D, be counted 
positive when it is in the same direction as that due to the glass 
ae alone, we have, since 8 + y =1, 
D,=(w—-1)t-(m- 1) B-(a- Dy = (4-1) t— (m1 - 1). 
Hence Dy = (pe pa) 0 oes ee (10) 
Equations (9) and (10) enable us to find 7 and p, if we know py 
and observe D and D,. Since by (9) and (10) 
joa Dp 
ee, Deo a ee 
* When a ray passes symmetrically through a prism, the deviation is given by 
sin 4(D+i)=sin $i. When 7 is small, we can write D+ i=yi or D=(u-1)%, but 
this result does not show how the want of symmetry affects the deviation. 
