in a new form of Refractometer. 397 
& Draw P’D parallel to & cs awe at hhh angles, and com- 
plete the rectangle BDP PC=i and DPP’=6. Let 
PP’=P, and the distance riba "thé abiienss at P’=2t. We 
have then 
t=t,+CP’. tan p=t,+P tan @~. tani, and 
A=2(t¢,+P tan @ tan 7) cos 9,-or 
Auce (¢, +P tan @ tan 7) (1) 
/1-+tan?7+ tan? 
We see that in general 4 has all possible values, and therefore 
pupil of the eye, for instance, the light which enters the eye 
from the surfaces will be limited to the small cone whose angle 
is bPa, and if the aperture be an mereney aad the differences 
in 4 may be reduced to any required degr 
It is proposed to find such a sabes. P. that with a given 
aperture these differences shall be as small as possible, which 
is equivalent to finding the distance from the mirrors at whic 
the phenomena of interference are most distinct. The change 
of J for a change in @, is 
64  _—-2(t,+ P tan ptan ec z (2) 
eT eee a 
— (1+tan? ¢+tan, 6g 
The ieee of td for a change in @% is _ 
<n oe 
_» (i + tan’ i+tan 0) Pty +P tan ptan jon (3) 
(1+tan? 7+ tan? 6)3 
For BA 6 we have 9=0 (or 4=0). 
60 
64 : 
For ai? we have (1+tan® 7+ tan? 6) Ptan p 
=(t, +P tan ptan?é) tan ?é, or 
: t ; 
(1 +tan? 6) P tan p=t, tan 7, whence ero tan 7 cos® 6 
Hence the fringes will be most distinct when @=0 and when 
ered J tan z (4) 
tan p 
This condition coincides nearly with that found by Feussner. 
If the thickness of the film is zero, or if the angle of hee 
dence is zero, the fringes are formed at the surface of the mir- 
rors. If the tilm is of baste thickness, the fringes appear at 
infinity. If at the same time g=0, and ¢,=0, or 7=0 and 
=, the position of the fringed is indeterminate. If 7 has the 
