H. F. Reid — Theory of the Bolometer. 



163 



q is the ratio of the resistance of the arm HI, when the strips 

 are exposed to radiation (their temperature then being t 2 ), to 

 their resistance when screened from radiation (their tempera- 

 ture then being t x ). According to Matthiessen's researches we 

 have, for small changes in temperature, 

 qR=R + a(t„ — tJiR 



q—l = ai{t a —t 1 ).* 



We may express (t„-t^) in terms of the quantities of heat 

 absorbed and given off by the strip. When the strip is ex- 

 posed to the radiation from a hot body, the heat falling on it is 

 increased ; we may, for convenience, consider that this latter 

 radiation falls on the strip in parallel rays, as it approximately 

 does. Let H be the increase of radiant heat passing unit area 

 at right angles to the direction of propagation in unit time. 



Fig. 2 represents the cross 



section of the strip; if A is 

 its length,f Ads an element 

 of the surface, d the angle 

 made by the normal to the 

 surface with the direction of 

 propagation of the radiation 

 from the hot body ; then 

 H cos dAds will be the in- 

 crease of heat falling on the 

 element Ads ; if a' and a" 

 are the average coefficients 

 of absorption for the differ- 

 ent angles of incidence act- 

 ually occurring, of the black- 

 ened and metallic surfaces 

 of the strip respectively, 

 the heat absorbed by the 

 strip in unit time will be 

 ^'JEU/cos dds+a"HAf cos dds, where the two integrals are to 

 be taken respectively over the blackened and metallic portions 

 of the strip, which are exposed to radiation from the hot body. 

 If ft is the breadth of the strip, cos dds=dft, and the expression 

 above becomes a / HAft / +a"JIAft" ; Aft' and Aft" are the projec- 

 tion as shown in fig. 2 of the blackened and ' metallic parts 

 respectively of the front surface of the strip. 



* a is not the coefficient determined by Matthiessen but can be readily calcu- 

 lated from his results. 



\ The bolometer strip is usually made of a number of narrow strips placed side 

 by side and connected in series. We look upon it as consisting of a single strip 

 bent back and forth; "k and fi' + fi" are the length and breadth the exposable 

 part would have if it were straightened out. 



