Prof. Forbes on Reflected Heat and Light. 481 



an equal part polarized — . Now, let the intensity of reflected heat 

 polarized in the plane of reflection (or — ), and that perpendicular 

 to it (or +), be represented by the following table, which contains 

 the quantities to be found. 



Table I. 



Incidence. Reflected Rays Polarized. 



+ 



0° Oo ho 



10 c, 6, 



20 c, b^ 



&c. &c. &c. 



Also let the quantities of heat actually observed to be reflected after 

 incomplete polarization by passing through a mica bundle, be the 

 following : 



Table II. 



Incidence. Polarizing Plane of Mica Bundle. 



+ - 



0° Ao Bo 



10 Ai Bi 



20 Aa B., 



&c. &c. &c. 



Now, the quantities A and B will be thus composed : The quantity 

 of heat transmitted by the mica bundle and incident on the reflecting 

 surface contains, when the plane of polarization is perpendicular to 



1 — p 



the plane of reflection, a portion of heat p ■\ —■ polarized + , 



an a portion of heat — ^ polarized — ; let these quantities be m 



and/?; then ?». + «= 1. Now, let the plane of polarization be 

 turned round 90'* ; then the part polarized in the j^lane of reflection 

 will now be m, and that perpendicular n. So that the heat is first 

 composed of a part m reflected according to the law of « in Table I., 

 and a part n reflected according to the law of b ; and then the con- 

 verse ; so that 



A^ = ma^-\- n b^ 



B,, = w a^ + m bg 

 Hence A, + B^ == a^ + b^ , as it evidently ought, and 



A^ — B^ = (m—n) (a^ — bj 

 Hence the differences of the columns in Table II. are in a constant 

 ratio to the differences of the columns in Table I. ; and as Table I. 

 may be computed from Fresnel's formulae 



tan "-(i-i o ^^j ?i!^l(ii:!^), 



tan- {i + i') ' sin'^ (f + i' ) ' 



the agreement or discrepancy will be apparent, and the coefiicient 

 (m — n) will indicate the polarizing power of the plates. Also, 

 since the sum of the numbers must be the same for both tables, a 

 single comparison would suffice to determine the index of refraction, 

 which must be assumed in computing the first table." 

 Phil. Mag. S. 3. Vol. 15. No. 98. Dec. 1839. 2 I 



