1 to Prof. Forbes's Researches on Heat. 



It now remains to explain how these observations have 

 been discussed. The ratio -^ is at once obtained by divi- 

 ding the second mean resuU by the first, and I have purposely 

 quoted these observations, to show how very nearly the plane 

 of polarization was thrown at right angles by the action of 

 this particular thickness of mica, especially in the case of dark 

 heat, which appears to be owing to its greater homogeneity, 

 as we shall presently have reason to infer. ^ 



We have seen above (art. 32) that 



£2 



pa = sm2 180° 



And therefore. 





sm-\ / E^ 



A 180° 



Since the radical has an ambiguous sign, the equation will be 



O ' c 



satisfied by a value of — — equal to a fractional number «, or 



by 1— a, or 1-f a, or 2— a, or 2 + a, or 3— a, &c. In the 

 case of the two examples given above, we have for the Argand 





^=l^ = -e29;\/^^=±'793 



And ^— ^ = -29 or '71 or 1-29 or 1-71, &c. 



A 



j^2 3'64< /E^ 



For the dark heat, ^^ = ^;^ = -915; Y -p2= ± '957. 



And — — = -41 or -59 or r4.1 or 1*59, &c. 



A 



The true value must be such, that, when a number of plates 



o—e 

 are employed, — — must increase uniformly with the thick- 

 ness of the plates. 



Clearly to mark this, and at the same time to combine the 

 results by graphical interpolation, I projected the numbers 

 obtained as above in the way shown in Plate II. fig. 1 . On 

 a horizontal line spaces representing the thickness of the plates 

 were set off as abscissae, and a few of the ambiguous values of 



as ordinates, which are marked by dots. It was then 



easy to select those points thus set ofi^, through which a 

 straight line could most nearly be drawn, representing the 



