ASTRONOMY 179 



increased or decreased in the same ratio, the resulting visual 

 sensations are no longer equal. Two intensities are considered 

 to produce equal photographic sensations when they produce 

 equal blackening or density in the same time or, in the case of 

 stars, discs of equal size. If the photographic sensations are 

 equal, it is assumed that the two intensities are equal. But 

 will the sensations remain equal if both intensities are increased 

 or decreased in the same ratio or if the common exposure-time 

 is increased or decreased ? In the first paper, the effect of a 

 difference in colour or wave-length of the two sources is in- 

 vestigated. 



In the study of this problem, it is the contrast phenomena 

 of the photographic plate which are of importance. The con- 

 trast, technically termed gafuma (7), is defined as the rate of 

 growth of density with logarithmic increase of exposure-time. 

 In astronomical applications the rate of increase in the diameter 

 of a stellar image with logarithmic increase of exposure-time 

 (termed astrogamma [f]), is more often used. Both constants 

 for a given type of plate depend somewhat upon developer and 

 degree of development. For similar conditions as regard 

 development, they depend further upon the emulsion and 

 upon the wave-length of the incident light. 



If for a given emulsion the densities are plotted as ordinates 

 against the logarithms of the exposures as abscissae, a " char- 

 acteristic curve " of the emulsion is obtained, and such curves 

 may be constructed for different wave-lengths. In general the 

 characteristic curve consists, first of a " toe " in which, near 

 the threshold sensitivity of the plate, the rate of increase in 

 density with time is small ; then, after a certain density, the 

 slope of the curve increases and remains nearly constant 

 through a wide range of exposure-time ; finally, for exposures 

 greater than a certain value, the slope decreases and finally is 

 reversed, denoting a stage in which increase in exposure results 

 in decrease in intensity. The slope of the straight portion of 

 the curve gives the value of the contrast (7) for normal expo- 

 sures. If the contrast is plotted against wave-length, the 

 curve obtained depends upon the emulsion. The contrast 

 increases with increase of wave-length in the blue region of the 

 spectrum, but after a certain wave-length the rate of increase 

 in general becomes smaller, and for some emulsions is then 

 followed by a decrease. The behaviour of astrogamma is 

 generall}^ similar. If, then, a blue star and a red star are found 

 to give the same photographic sensation for a given exposure- 

 time and the exposure-time is increased, the resulting sensations 

 will not in general be equal, owing to the dependence of 7 and 

 r upon the wave-length. Also two other stars, blue and red, 

 whose magnitudes are greater or less by the same amount 



