OF ARTS AND SCIENCES. 391, 



Table II. gives the percentage of light transmitted by 1,4, and 10 

 plates for different values of i. The first column gives the values of i; 

 the second, fourth, and sixth columns give the observed amounts of 

 light transmitted ; and the third, fifth, and seventh columns give the 

 theoretical amounts. These last were calculated from the formula 



t = 1. ( — , ', — 7 4- , , ~ ,. ,. ) , in which A was determined 



■^ \\-\-[ia — \)A^^\-\-{m — \) Lij' 



from the equation A = ^!"" ,~^ , and B from the equation B =■■ ■ 



^^^^., ,~^l , by substitutino: the proper values for the angles of inci- 

 tang- (j-j-r)' •' o k- f & 



dence and refraction, assuming the index of refraction to be 1.55. 

 Constructing the points, with abscissas equal to the angles of incidence 

 and ordinates to the observed amounts of light transmitted, it will be 

 found that they form very smooth curves. But it will be noticed that 

 while they agree in general with the theoretical results, assuming tliat 

 the light is lost by simple specular reflection, the differences are con- 

 siderable, showing that we ought not in our calculation to neglect the 

 opacity of the glass, imperfection of the surface, and other sources of 

 error. 



From the numbers in this table, we conclude that, while the amount 

 of light transmitted by one plate decreases considerably as ^ increases, 

 the amount transmitted by four plates is more nearly constant for small 

 angles, and the amount transmitted by ten plates actually increases 

 until i becomes 55°; which facts agree with the conclusions arrived at 

 theoretically by Prof. Pickering. (Proc. Amer. Acad. Vol. IX. p. 6.) 



It was impossible to carry these experiments beyond i = 65° with 

 the apparatus employed, because the disc came so near the mirror as 

 to cast a shadow upon itself. 



