W. B. Rogers on Binocular Vision. 91 
m:RL=ar: Ra+ar, 66. 
, a 
whence RL—am:am=Ra: ar, fe 
and therefore 
< — By a like process also, 
c.cn 
R 
we have cs= 
R 
Since in these experiments, a m and 
nm are very small compared with R L, 
they may without material error be ex- 
punged from the above values of ar 
and es ; and since the distance ac must 
always be inconsiderable compared 
with Ra or Re these two lines ma 
be assumed. as sensibly equal and par- 
allel, and as a consequence of the lat- 
ter the angles bar and des may be 
taken as equal. With these qualifica- 
tions, the former values when compar- |, 
ed with one another give us the pro- rik aes 
portion, ar :cs=am cn. | Ry 
f now the two figures binocularly 
combined be of such construction that 
the corresponding breadths are in a * 
ae 
= 
——~ 
j 
= 
nstant ratio, we will have 
ig :cd=mb : nd, % 
whence am:icn=ab: cd. pase es 
This compared with the former proportion gives z 
ar:ics=ab:cd. , 
_ But we have seen that the angles at a and care practically 
equal, therefore the line ds is parallel to 7, and as its end d lies 
in the plane of zyr, the whole line must lie in that plane. Con- 
- Sequently the resultant point s is situated in the plane of ry. 
fn the same way it may be proved that any other resultant points 
similarly formed must be situated in the plane of zyr. Hence 
