222 STELLAR PHOTOGRAPHY. 



seen. With the eight-inch lens DM. +89° 37 and a were distinctly separated in 

 the original negative. This is a satisfactory proof of the good definition of a lens 

 of so short a focus. 



MlSCELLATTEOUS. 



The different photometric processes which have been used in determining the 

 light of the stars give results which differ systematically when large variations in 

 light are to be measured. In the Harvard Observatory Annals, Vol. XIV. p. 504, 

 it is shown that the systematic variations of the best catalogues exceed one fifth 

 of the entire intervals measured. In other words, if a great number of pairs of stars 

 are selected, whose average difference in brightness is five magnitudes according to 

 one catalogue, the difference will be only four magnitudes in another. This is also 

 true when the logarithms of the lio;ht are used. It is not due to a difference in the 

 assumed value of the unit of the scale of magnitudes, but to an actual difference 

 in the measurement of the amount of light. In the case assumed above, if the light 

 of the brighter star is taken as 100, that of the fainter star according to one cata- 

 logue will be 1 ; according to the other, it will be 2.5. Evidently, large errors affect 

 one or more of the catalogues compared, which cannot be eliminated by increasing 

 the number of observations. The best way of determining which is probably correct 

 is to repeat the measures by a variety of entirely different methods. Photogra- 

 phy affords an excellent means of doing this, since the errors, if any, will be of a 

 very different kind. Several methods may be employed, each giving an independent 

 test. The construction of a standard scale, as described on page 211, gives a direct 

 measure of the ratio of the light of two stars of the same color, if we can assume 

 that the brightness of the image is proportional to the area of the object-glass. The 

 principal objection to this method arises from diffraction, which enlarges the images 

 when the aperture is very small. A defect in the portion of the plate on which the 

 standard is photographed might affect all of the measures. This should be tested 

 by measuring all the stars on a plate which has received several exposures with 

 various apertui-es. The results also give a good means of studying the effect of 

 aberration at different distances from the centre of the plate. Instead of varying 

 the aperture, we may vary the time of exposure. This may be accomplished by 

 varying the rate of motion of the image. For stars in the vicinity of the pole, the 

 velocity is proportional to the polar distance. If, as on page 187, we assume that 

 the brightness of a star capable of producing a given impression will vary as the 



