sensitiveness in Detectors of Radiant Heat. 67 



so that X is a quantity that depends on the kind of galvanometer 

 used and on the magnetic field, but not on the gauge of the wire 

 with which the galvanometer is wound. 



Also let the heat lost from a face of the pile by radiation and 

 convection be kd per sq. cm. per sec. in accordance with Newton's 

 law of cooling. 



3. The sensitiveness is evidently increased by increasing the 

 absorptive power of the faces, and also, on account of the 

 diminished resistance, by increasing the cross-section of the bars 

 at the expense of their insulation. 



We will assume that the faces of the pile are perfectly black, 

 and that the thickness of the insulation is negligible, so that 



A = n (Aj + A 2 ). 



Equating the heat gained to that lost we have : — 

 for the face on which the heat is incident, 



HA = k6 x A + (0, - 2 ) n (A^ + A 2 o- 2 )/Z + nTeC/J; 

 for the other face, 



= k0 2 A - (d 1 - 2 ) n (A l0 -a + A 2 o- 2 )/J - nTeC/J, 

 where / is Joule's equivalent, = 4*2 if e is in volts. 

 Subtracting and rearranging, 



HA - 2nTeC/J 

 1 2 ~ kA + 2n (A^ + A 2 <r 2 )/Z " 



The electromotive force is ne {0 X — 6 2 ), and the resistance of 

 the pile and galvanometer is 



nl( Pl /\ + p 2 /A 2 ) + G } 



so that 



HA - 2nTeC/J Tie 



~ kA + 2n (A l0 - 3 + A 2 o- 2 )/Z " nl (pj^ + p 2 /A 2 ) + ' 



Solving for and inserting in the formula for the deflection, 



& = X7T e - nA*/G 



€ {kA+2n(A 1 cr 1 + A 2 a 2 )fl} {nl(p 1 /& 1 +p 2 /& 2 )+ G} + 2n*Te*/J' 



s is of the form 

 cG = b, and 8 = a/2 \lbc. 



n I C 



This is of the form h = 1 ~ , and therefore for a maximum 



o + Cbr 



5—2 



