188 STELLAK PHOTOGRAPHY. 



refraction. "With a given aperture, these variations may be regarded as causing a 

 constant angular deviation of different portions of the beam ; d will therefore be 

 proportional to /. It will also increase rapidly if a increases. Secondly, sphei-ical 

 and chromatic aberration of the lens. This will have the same angular value in 

 equally perfect lenses, so that when ^ is constant it will be proportional to /. Its 

 angular value will increase rapidly as a increases. Thirdly, diffraction from the 

 edges of the lens. This error is ordinarily small, and, unlike the other sources of 

 error, increases as the aperture diminishes. Fourthly, a chemical action occurs by 

 which a decomposition of the salts of silver, at the point exposed to the light, 

 extends to the adjacent particles. This effect is very marked in the case of the 

 bright stars, and is of course independent of the dimensions of the lens. The 

 increased size of the images of the bright stars is in part only due to this chemical 

 action. It is also caused by the light diffused by the other sources of error men- 

 tioned above, and by the light reflected from the back of the plate. In the faint 

 stars this chemical action is inappreciable, but becomes perceptible when the light 

 is intense. It is therefore very difficult to compare two lenses theoretically, even 

 if we are sure that they differ only in their dimensions. If we assume that d is 

 a constant, so that the fourth of the above causes is the principal one to act, I will 

 depend only on the aperture of the object-glass. Since one magnitude corresponds 

 to a ratio of light of 2.512, an increase of the aperture of 1.585 should permit stars 

 one magnitude fainter to be photographed in the same time. In like mannei-, 

 increasing the aperture ten times should extend this limit by five magnitudes. In 

 reality this is far from being the case, the actual increase in aperture required 

 being much greater. Again, if the angular diameter of the images is nearly con- 

 stant, it will be proportional to /, and I will remain the same as long as the angular 

 aperture ^ is constant. On this hypothesis similar lenses, whether large or small, 

 could photograph equally faint stars. The fact lies somewhere between the two, 

 and perhaps it would not be far from the truth to assume that the limiting amount 



of light was proportional to -r^. When the positions of the stars are to be meas- 

 ured, a large telescope has a very great advantage. The scale is proportional to 

 the focal length, and, since the errors of measurement are nearly constant when 

 expressed linearly, this effect will be inversely as the focal length. 



The second case to be considered is that in which the image of the star is slowly 

 traversing the plate. Let v equal the velocity, or distance traversed per second. 

 Then the time of exposure will equal that required by the star to move a distance 



