H. F. Reid — Theory of the Bolometer. 165 



Write /3 / +y3 // =/3; our three cases give : 

 I. A'=/9'=0; P"=P; A"=2;£; 



and *-^ 



<\/2m" 



II. A"=/3"=0; ?=$; A'=2;/3; 



and o oo — — — . 



III. 0"=O; ^=j3'; !A'=A"=;i0; , 



and £ 3 



VW -f m" 



Suppose a black body, with coefficients of absorption and 

 emission, a' and m', to be placed in a stream of radiant heat 

 of intensity H, its rise in temperature will be given by the 

 expression (t 1 -t )=H.a , /2m ! ; if the same body should have 

 a bright surface with coefficients a" and m", its rise in tem- 

 perature would be \t-t^\=Ha" l%m" . Experiments with black- 

 ened and unblackened thermometers show that [^-^J < (t-t ) ; 

 . * . a"\m" '<Ca'/m' ; we also know that a" <V, and m" <jrb' ; we 

 see therefore that d 1 <C.d 2 <id s . 



The eq. (3) can now be written 



DorHM 



6=— — va/5^-0; (4) 



where M stands for a"/V2m", a'/V^mf or a'/Vm'+m", accord- 

 ing as our strip belongs to case I, II or III. 



In this expression for d, D depends for its value on the form 

 of the galvanometer, etc., as already noticed ; a is ratio of the 

 increase in resistance of platinum for one degree change of 

 temperature above t , to its resistance at temperature t Q . 

 Matthiessen found that this coefficient did not vary much for 

 different met'als. H is the intensity of the radiation to be 

 measured. M has its greatest value when the front of the 

 strip is very black and the back very bright ; i can be given 

 its greatest value by having the largest possible part of the 

 strip exposable, and making the resistance of the rest of the 

 branch Mi very small. Since the resistance of the strip does 

 not enter the equation, it is of no importance so long as the 

 four arms of the bridge and the galvanometer all have the 

 same resistance ; but this should not be so small as to decrease 

 materially the value of i, or to make the galvanometer connec- 

 tions an appreciable fraction of the resistance in the galvano- 

 meter branch. I and /? only occur multiplied together and 

 under the radical sign ; other things being equal d varies as the 

 square root of the exposable area of the strip ; for a given 



