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



The temperature of the strip will be constant when the heat 

 developed by the current plus the heat absorbed equals that 

 lost by radiation and convection plus that lost by conduction, 

 C 2 ; i. e. when 

 (AW + A"m") ft - + C 1 + a'HA/5' + a"BX/3" = 



(A'm' + A"m")(t-t ) + C i ; 

 _ (AW + A"m") ft - 1 ) + H Ma'/3' + a"/3") +0,-0 , 

 2 °~ A'm' + A"m" 



and 

 q -l = ai(t-t l ) = ai\(t-t )-(t-t a )\ = 



ai{H\(a'p' + a"/3")+C 1 -GJ 



A'm'+A"m" 

 Introducing this value in eq. (2) we obtain 



ty= D«{m(a^ + g " ) 8")+C 1 -C,}V?ft=g 

 4VA'm' + A"m" 

 H/l(« / i 5'4-« // j3 // ) is the quantity of radiant heat absorbed by the 

 strip ; a' and a" will be greatest when every element of the 

 exposed surface of the strip is at right angles to the direction 

 of propagation of the radiant heat ; i. e. when the front sur- 

 face of the strip is 'flat. A'm'-\-A"m" is the heat lost from 

 the whole surface of the strip in unit time when its tempera- 

 ture is one degree higher than that of the surrounding air and 

 case. Other quantities remaining the same, this will be smaller 

 and o larger as A'-f A", the whole surface of the strip is 

 smaller. C x and C 2 are smaller, the smaller the cross section 

 of the strip. The less metal in the strip for a given exposed 

 surface the more rapidly will it reach its temperature equilib- 

 rium when exposed to radiation. All these considerations 

 show that it is best to make the strip very thin. 



If the strip is so thin that a further decrease in its thickness 

 would only diminish the amount of heat given off by it by a 

 small fraction of this amount, it does not appear that any 

 advantage would be gained by making it thinner. In the case 

 of a strip l mm wide the limit is probably fully reached when 

 the thickness* is 0-01 mm . 



Let us now determine how much of the strip should be 

 blackened. There are but three practical cases : 



I. None of the strip blacketied. 



II. The whole surface blackened. 



III. The front surface only blackened. 



Referring to eq. (3) we see we need only consider the termf 

 X{a'/3' + a"/3") 



A/A'm' + A"m"' 



* In Professor Langley's instruments the thickness lies between - 01 mm and 

 - 001 mm . See his paper l, 0n Hitherto unrecog. Wave-lengths/' cited above, 

 f We suppose the strip to be thin enough to allow us to neglect Ci and C 2 . 



