STELLAR PHOTOGRAPHY. 187 



being at rest, photographing the trails of the stars ; secondly, with the aid of clock- 

 work, forming charts ; and, thirdly, photographing the spectra of the stars. These 

 subjects will be considered in three separate sections. 



Theoretical Coxsideratioxs. 



The first case to be considered is that of a luminous point at rest. The formation 

 of a chart of the stars when the instrument is perfect!}" adjusted is an example of 

 this case. Secondly, let the luminous object be a line instead of a point. A moving 

 luminous point, as a star when the telescope is at rest or the adjustment is imperfect, 

 will be considered in this connection. The third case is that of a luminous surface, 

 as a nebula or comet. 



To compare the advantages of different forms of instrument, a discussion is given 

 below to show the relation between the dimensions of the lens employed and the 

 light of the faintest star that can be photographed with it. 



The following notation will be used : — 



a = aperture of lens. 

 / = focal length of lens. 

 / = proportion of light transmitted by lens. 

 d = diameter of the photographic image of the faintest star capable of impressing 



itself upon the plate. 

 m = brightness of such a star expressed in stellar magnitudes. 

 / = ratio of the light emitted by such a star to that of a star of magnitude zero. 

 T = time of exposure. 

 s = sensitiveness of plate measured by the amount of light required to produce 



the faintest perceptible photographic impression. 



The value of I will be proportional to '/- and to ,?. inversely proportional to «® and 

 to i, and may be assumed to be inversely proportional to T. This last assump- 

 tion is based on experiment, and seems to be justified within wide limits. Then 



I = A -ijj-- in which A is a constant dependent on the units emjiloyed to indicate 

 the magnitudes of the various quantities involved in this equation. Upon Pogson's 

 system of magnitudes, m = —2.5 log /, and hence 



m = —2.5 (log A+2\ogd-\- log -s — 2 log a — log t — log T). 



The uncertainty in the value of d renders it difficult to compare results in differ- 

 ent cases. The principal causes affecting it are, first, variations in the atmospheric 



