BERNARD L. STREHLER 255 



the total rate of emission of all frequencies we find 



Total rate = (c/'2) I pidv, = ^ 





If /u'* is considerably larger than kT but still small compared with vo 

 and if (C) = (D), we can obtain the approximate result, 



Total rate ^ ^ a ^ j^o' e-'^'^/^^ 

 2 h 



= 5.7 X 10-''5vo^e-'»'*/^-^ watt/cm2 



where lo is expressed in sec.~^. 



Let us take vq = 0.57 X 10^^ sec.~^ (equivalent to a wavelength of 

 5300 A) and hv* = lOkT. At 300° K this corresponds to emission at a 

 wavelength less than 4800 A, which is 500 A beyond the expected 

 threshold. We find a possible rate of emission of about 5 X 10 ~^ 

 watt/cm-, equivalent to about 10^^ quanta per second per square 

 centimeter. This is to be compared with the normal emission by a 

 black body of radiation having quanta whose energy is more than 

 lOfcT, which comes to only 5.8 X 10" ^ watt/cm- at 300° K. It corre- 

 sponds to a relatively bright light, though not very much brighter than 

 the observed maximum brightness of a concentrated suspension of 

 luminous bacteria or other bioluminescent organisms, being of the 

 order of the brightness of a white surface one meter distant from a 

 40-watt tungsten lamp. The total possible rate of emission beyond 

 4690 A, however, is 5 X 10 ~*^ watt/cm-, and that beyond 4600 A is 

 5 X 10 ~^ watt/cm-. The luminescence of luminous bacteria does not 

 drop off this rapidly with decreasing wavelength, and it would be 

 interesting to see if the actual emission at short wavelengths surpassed 

 the theoretical upper limit. 



References 



Mott, N. F., and I. N. Sneddon. 1948. Interaction of radiation with matter. 



In Wave Mechanics, chapter 10, pp. 247-90. Oxford University Press, 



London. 

 Spruit-van der Burg, A. 1950. Emission spectra of luminous bacteria. Bio- 



chim. et Biophys. Acta, 5, 175-78. 



