286 Dr. Herschel's Experiments for investigating 
These things being premised, I proceed to explain the con- 
sequences that must arise from the mixture of the transmitted 
with the originally reflected rays. The first is, that the rays 
which after transmission re-enter the prism at different points, 
and are the cause of the streaks, will not proceed in a parallel 
direction with those that by reflection from the same or neigh- 
bouring points form the blue bow. For instance, let A a a ! , 
and B (3 jQ 7 , fig. 13 , be two incident and reflected rays of the 
blue bow ; then if the yellow ray transmitted at a after two 
refractions, and one reflection, not expressed in this figure, 
re-enters the prism at y, it will make the angle y' y F equal to 
the angle AaG. But from the construction of the blue bow, 
it has been shown that B (3 G is greater than A « G ; /3' (3 F 
is therefore greater than y'y F, and the rays (3 (3' and y y' will 
meet somewhere in the line (3 (3' produced. If we call the 
greatest of the two angles m, the smallest n , and the distance 
of the angular points d, then d x — -jdL-. will give us the 
length of the line (3 (3', at which the two rays will meet and 
intersect each other, which according to the enlarged size of 
this figure, will be at 773 inches from (3. For the same rea- 
son the orange ray 0 o' will meet f3 (3' at 1084 inches, and the 
red ray r r' at 1401 inches from (3. It follows also from the 
same construction, that some of the transmitted rays will di- 
verge from the reflected ones ; for instance, the green ray 
transmitted at a, which re-enters the prism at g, will make 
the angle g' g F less than the angle (3' [3 F ; the rays (3 (3‘ and 
g' g will therefore diverge. To this may be added, that gg' 
y y' 0 o' rr f and u a! will be parallel. 
If such difference between the directions of the transmitted 
