] g(j PROFESSOR FORBES'S RESEARCHES ON HEAT. 



32. Recalling, then, Fresnel's formula, quoted in art. 70 of the First Series, 

 we have 



E2 „ f O 



p2 = sin2 180° 



{-} 



where F^ is the intensity of the whole incident polarized ray ; E^ the intensity of 

 that portion which, after transmission through the depolarizing plate, is capable 

 of being analyzed in a perpendicular plane. These two quantities being deter- 

 mined from observation, the fii'st side of this equation, or their ratio, becomes 

 known. On the second side we have two quantities, either of which may be as- 

 sumed, and the other becomes known, viz. o — e the retardation of the one doubly 

 refracted ray upon the other within the crystal, and x the length of a wave. Now, 

 it is obvious from the form of the expression, that an infinite number of values of 



^^^ will satisfy the equation ; in light there can be little ambiguity arising from 



this cause, because the phenomena of periodic colours at once afford the means of 

 selecting the true solution. In the case of heat, we must proceed with more cau- 



tion, the value of —^ being wholly unknown ; we only assume (as we are en- 

 titled to do) that this quantit}^ increases uniformly with the thickness of the 

 plate, which it necessarily must, since the retardation is as the thickness, and x is 

 independent of it. By a very simple process, the true value was easily selected. 



33. Five depolarizing mica plates, of different thicknesses, of exactly the 

 same quality, and each as uniform as possible, were provided. They w^re cut to 

 the same size, and of such a form that each could at once be placed with its neu- 

 tral axis (a line in the plane passing through the two axes of double refraction) 

 vertical, or inclined 45° at pleasure. Their thickness was next to be determined. 

 The examination of the colours shewn by polarized light was the most obvious 

 method, but not susceptible of the exactness which was required. It was, how- 

 ever, used as a check. These colours were : 



Retardation in Millionlhs 

 of an inch.* 



No. 1. White inclining to yellow, 12 



No. 2. Rich blue, 28 



No. 3. A blue purple, -18 



No. 4. Between red and orange, 36 



No. 6. Pink, 80 



34. The relative thicknesses which these numbers afford, are tolerably veri- 

 fied (excepting the first) by the following results of actual measurement, by means 



* These numbers are obtained by doubling those due to the corresponding tints of thin plates of 

 air in Newton's Table. In the case of the two last numbers, there might have been some doubt as to 

 the order of colours to which they belonged, but this was removed by the measurements given farther 

 on, which shewed that the pink of No. h. is a colour of the fourth order. 



