ASTRONOMICAL PHOTOGRAPHY ' 751 



the contraction or shrinkage of the photographic gelatin emulsion during the process 

 of development and drying. Extensive investigations have been made to determine 

 the degree of uncertainty which may be introduced on this account through the use of 

 the photographic film in astronomical astrometry. Schlesinger in 1906 concluded 

 from extensive investigation that the amount of error of measurement in photographic 

 plates which could be attributed to distortion were in general of the order of about 

 + 0.009 mm. (average mean error). The corresponding mean error in the observer's 

 bisection of a star image was calculated to be ±0.0020 mm. 



The subject of film distortion has also been investigated bj* S. Albrecht, Perrine, 

 Ross, and others. All conclude that the amount of error likely to be introduced by 

 distortion on the photographic film mounted on glass is small compared with errors of 

 bisection of the image by the measurer. It is, perhaps, worth mention that a series 

 of tests by F. E. Ross in 1912 gave for the probable error of the measured distance of 

 air-dried plates +0.0020 mm., while the probable error of a measured distance on al- 

 cohol-dried plates was + 0.0012 mm. It would appear that uniformity of drying, a feat 

 which is accomplished very effectively by immersion of the plate in alcohol, is an 

 important factor in keeping film distortion to a minimum. This has been established 

 at least for plates of small dimensions, such as the 27 by 37 mm., used in the investiga- 

 tion by Ross. 



Photographic Photometry.— Fxom the introduction of the dry plate into astronomy 

 it was early sensed that the size of the stellar image upon the plate might be taken as 

 an index of the brightness or magnitude of the star. In the year 1857 Bond of the 

 Harvard Observatory demonstrated an empirical relation between the exposure time t 

 and the diameter y of the photographic image which he represented by the equation 



P +Q =y^ (10) 



In the formula P and Q are constants of the plate used. Later investigations by 

 Charlier showed that a close agreement between stellar magnitudes and measured 

 diameters followed if the relationship were expressed logarithmically by the equation 



m = a — h log 10 d (11) 



where m is the magnitude and d the diameter of the stellar image, a and h being plate 

 constants. 



At the Royal Observatory in Greenwich a similar expression involving a square 

 3-oot relationship was found to be applicable to a wider range of conditions as regards 

 plates and instruments than could be satisfied by the logarithmic expression. 

 Accordinglj^ the following form, well known in many observatories, has found wide 

 acceptance : 



VI = a - hx^d (12) 



In utilizing this formula for the calculation of magnitudes of stars from their 

 photographic images, some instrument of precision such as the micrometer microscope 

 is utilized in measuring the value of d, the diameter of the stellar image. The quan- 

 tities a and h are constants of the plate which may easily be determined from simul- 

 taneous equations when two or more stars of known magnitude m are photographed. 



Since the photographic image of the star at best shows no well-defined periphery, 

 the principal source of error in measuring is the uncertainty of locating the extremities 

 of the diameter to be measured. It is customary in measiirement to measure two 

 diameters at right angles to each other and to take the mean. This is particiilarly 

 necessary if through poor guiding or optical difficulties the images are at all elongated. 

 Experience shows that even the same eye may pass different judgments on large 



