foote: pyrometer color screens 529 



integrator No. 1. Surprising accuracy is obtainable in measur- 

 ing \. This is evident when one considers that the hnninosity 

 curve for a good red glass extends only from about X = 0.600 

 to 0.750 n. Since all errors are actually based on the difference 

 of these two wave lengths, a low precision in the determination 

 of the center of gravity as far as the curve is concerned still 

 means a very high precision in the determination of the absolute 

 value of \g. Four or five significant figures are obtainable. 



The method of determining X^ suggested by Hyde involves 

 the log ratio of the areas of two luminosity curves, and when 

 \l is expressed by equation (5) its determination requires the 

 ratio of the areas of two curves. In general the area of luminosity 

 curves can not be measured by a planimeter with an accuracy 

 much better than 0.5 per cent; and since a direct mathematical 

 integration is impossible, because T = /(X) and V = f(\) are 

 not expressible by any usable equations, it is evident that 

 great precision is not readily possible in the determination of X^ 

 by such a method — probably not better than three significant 

 figures when great care is taken. 



Inspection of equation (5) however shows a very curious re- 

 lation. Suppose that instead of plotting X versus JTV as ordi- 

 nates, the ordinary luminosity curve, we plot JVT /\ as ordinates. 

 The line of the center of gravity of this curve is given by the 

 following expression : 



(7) X (center gravity) = "^ 



J 



ill A 



which is identical with (5'> 



Therefore the true effective wave length of the pyrometer 

 glass is the wave length corresponding to the center of gravity 

 of the curve /(X) = JVT/\, i.e., the luminosity at any wave 

 length divided by the wave length. The true value of X^ is 

 slightly different from the value of X^. The center of gravity 

 of the curve JVT :\ versus X can be determined with great 

 accuracy, so that a curve of X^r = fid) may be easily obtained by 

 this method. Whether such high mathematical accuracy is 



