THIRD SERIES.— REFRANGIBILITY OF HEAT. 



195 



.M 



What is true of one ray GD, which after refraction meets the posterior surface at 

 K, its middle point, will be true of any other parallel to it ; also the incident and 

 emergent rays DG, EH, form equal angles 

 with the surface AB when the angles A and 

 B are equal. By h3^othesis DKC = the angle 



of total internal reflection = sin~^-=/3. 



Let KD^, the angle of refraction, = s, then 

 sin a = /* sin ^. Also, considering « positive 

 when G falls between L and C, and the cor- 

 responding value of g also +, we have in the 

 triangle KDC 



180° = y3 + ACK + (90° + g) 



And, calling the angle at C, I, ACK = ^I, 



90° = /3 + |I + g. 

 But sin « = (It sin g = (tt sin (90° — (^ + il)) 



= i^ cos (/3 + |I) 



= («* {cos /3 COS |I 



(Also since sin /3 = i,) 



Whence 



sin ^ sin ^1} 

 sin "^fi cos |I — sin /3 sin |I} 



= /^] \/l_^cos|I sin|ll 



= Vjtt^ — 1 cos ^I — sin |I 



=yi+( 



sin oi -\- sin ^I 

 cos 1 1 



y 



54. I had a rock-salt prism constructed, so that the incidence on the first 

 surface might be nearly vertical at the critical angle of total reflection, so as to 

 avoid as much as possible any error arising from imperfections of the surface, or 

 want of absolute equality of the angles at A and B ; and likewise, that within the 

 limits of the experiment, the loss of heat by reflection at the two surfaces might 

 be nearly unaltered, as it is believed to be almost constant at incidences tolerabl}^ 

 nearly perpendicular.* This prism, constructed for me by Mr John Adie, had 

 two angles of 40° and one of 100° ; and so accurately was it made, that (satisfy- 

 ing myself with a careful measurement by the common goniometer, extreme 

 nicety being unimportant) the angles appeared to be true to those quantities 

 within a few minutes of a degree. 



55. By a reference to Plate XIII, Fig, 1, it will now be understood that the 

 required arrangement is of this kind. The heat diverging from the source S, is 

 converted into an approximately parallel beam by the lens L. It then passes 



* See Melloni on the Reflection of Heat, Annates de Chimie, Dec. 1835. 



