92 Mr. Earnshaw on a new Experiment 
The third and last point relates to the difficulty which might 
arise from the consideration, that if the ring is of such enor- 
mous dimensions, and if the portion of it opposite that in 
which we are placed is so very far from us as we must sup-~ 
pose it to be, how does it happen that the light of that portion 
is not much less than that of the part nearest to us? To ac- 
count for this effect, let us suppose the point of the interior 
edge of the ring S, in which the solar system is placed, to be 
the common vertex of two opposite cones of small and equal 
vertical angles (fig. 2), each produced respectively to the outer 
edge of the: ring. The visual angles under which the two oppo- 
site portions of the Milky Way intercepted by the two cones 
will be seen will be equal ; that is to say, the two portions will 
appear equal: but a much greater number of stars will con- 
tribute to the illumination of the furthest portion, inasmuch 
as the section made by the cone is much greater at that di- 
stance, whereas a smaller number of stars will contribute to 
illuminate the nearest portion. ‘The greater quantity of stars 
giving light will thus compensate to a certain extent for the 
greater distance, and the brightness of the Milky Way can- 
not differ a great deal in its different parts. 
To this cause we must add, that, if the sun be not really on 
the edge of the ring, as probably it is not, but there be other 
stars between it and the empty space within the ring, they 
will necessarily tend to increase in a slight degree the bright- 
ness of that portion of the Milky Way which is opposite to 
the constellation of the Cross. 
XIV. On a new Experiment in Physical Optics. 
By the Rev. S. Earnsuaw, M.A., Cambridge*. 
Y a train of reasoning confessedly obscure, but neverthe- 
less founded essentially on a theory of undulations, Fres- 
nel obtained the following formule. for the amplitudes of the 
vibrations of light reflected at the surface of a medium of no 
double refraction, viz. 
hai.) ee 
4a Gara) A CAN ath 2 ee 
sin (7+7) tan (7+2’) 
the former (A) for light polarized in the plane of reflexion ; 
and the latter (B) for light polarized at right angles to the 
plane of reflexion. It ought not to be reckoned an insupe~ 
rable objection to the reception of these formule, were they not 
found to give the exact degree of brightness observed in ex- 
periments. More stress may however ‘be laid upon the neces- 
. (B) 
* Communicated by the Author. 
