OF NEWTON'S RINGS BEYOND THE CRITICAL ANGLE. 



653 



mode of disappearance of the rings, and to determine their greatest dilatation, we should have to 

 enter on a special investigation in which the inclination of the surfaces should be taken into 

 account. 



20. I have calculated the following Table of the intensity of the transmitted light, taking the 

 intensity of the incident light at 100. The Table is calculated for values of D increasing by \\, 

 and for three angles of incidence, namely, the critical angle, the angle i before mentioned, and a 

 considerable angle, for which I have taken 60". I have supposed ij. = V63, which is about the refrac- 

 tive index for the brightest part of the spectrum in the case of flint glass. This value of fj. gives 

 'y = 37''5]', I = 42° 18'. The numerals I., II. refer to light polarized in and perpendicularly to the 

 plane of incidence respectively. 



2! . A Table such as this would enable us to draw the curve of intensity, or the curve in which 

 the abscissa is proportional to the distance of the point considered from the point of contact, and the 

 ordinate proportional to the intensity. For this purpose it would only be requisite to lay down on 

 the axis of the abscissa;, on the positive and negative sides of the origin, distances proportional to the 

 squares of the numbers in the first column, and to take for ordinatcs lengths proportional to the 

 numbers in one of the succeeding columns. To draw the curve of intensity for i=i or for i = (kf, 

 the table ought to have been calculated with smaller intervals between the values of D ; but the law 

 of the decrease of the inten.sity cannot be accurately observed. 



22. From the expression (13) compared with (4), it will bo seen that the intonsity decreases 

 much more rapidly, at some distance from the point of contact, when i is considerably greater than y 

 than when i = y nearly. This agrees with ol)scrvati()n. Wiiat may be called the rnpged edge of 

 the l)riglit spot seen by transmission is in fact mucli broader in the latter c.i.se than in the former. 



When i becomes equal to 90° there is no particular change in the value of 7, but tlie angles Q 

 and (j) become equal to fjo", and therefore sin 20 and sin 2f/) vanish, so tli.it the spot vanishes. Ob- 

 servation shows that the spot becomes very small when i becomes nearly equal to yo". 

 Vol. VIII. Part V. 4 1' 



