162 H. F. JReid — Theory of the Bolometer. 



If the branch R contains this strip, 1=1. What is the best 

 value to give nl When n varies from 1 to 0, l/^/l+n varies 

 from about 0*7 to 1 ; so that there is not a great advantage in 

 making n less than 1 ; and there is a decided disadvantage. 

 The currents in the branches R and S have the ratio v/(u—v)= 

 S/~R=n ; the heat developed in R is v 2 R; that in S is -y 3 R/^; 

 if n is much less than unity, this becomes very large, the tem- 

 perature of the branch S is raised too high and irregular move- 

 ments of the needle are produced. If, on the other hand, the 

 branch IS contain the covered strip, n=l ; the heat developed 

 in R and IB, have the ratio R/£R = l/£; reasoning as above we 

 conclude that in this case the most desirable value of I is unity. 



To summarize : the bridge should be so arranged that l=n=l; 

 the galvanometer resistance G should equal that of the bolo- 

 meter strip R ; B and E have disappeared from the equation ; 

 their actual values are therefore unimportant so long as v is 

 fixed. This is applicable to the case in which we wish our 

 instrument to have its greatest sensitiveness. If the quantity 

 of radiant heat to be measured is so great that this is not 

 desired we can diminish the sensitiveness by decreasing v or T> 

 or by adding a resistance to the galvanometer branch ; it will 

 usually be found advisable to chauge the first two quantities. 



Let us now consider the strip itself. As the intensity of the 

 current v is limited by the excess of temperature over that of 

 the surrounding air to which we can raise the bolometer strip 

 without producing inconvenient movements of the galvano- 

 meter needle, it will be convenient to replace v by its equiva- 

 lent in terms of this excess of temperature. Let i be the ratio 

 of the resistance of the exposed part of the strip to that of the 

 whole arm in which the strip is ; let t be the temperature of 

 the air and the enclosure surrounding the strip ; t yJ the tem- 

 perature of the strip when the current v is passing through it ; 

 m'(t-t^) and m"{t-t^) the loss of heat by radiation and con- 

 vection per unit time per unit area of the blackened and me- 

 tallic surfaces of the strip respectively (according to Newton's 

 law of cooling, which is sufficiently accurate for the small 

 changes in temperature under consideration) ; A' and A", the 

 areas of these surfaces. We here suppose only a part of the 

 strip to be blackened. The temperature of the strip will be 

 constant when the amount of heat generated by the current 

 equals the amount lost from the surface and by conduction, C 1 ; 

 i. e. when 



v*i'R=(A'm' + A"m")(t-t )+C 1 . 



Putting the value of v derived from this equation in eq. (1), 

 we find, writing l=n=l, 



S== V (Q l) V(A'm' + A" m ")(t l ^tJ+C 1 ^ 

 4 ^ ' /^i 



