304 SCHLESINGER— PHOTOGRAPHIC DOUBLET [April 24. 



with proper precautions, these fears are groundless and that this 

 form of instrument is admirably adapted for cataloguing purposes. 

 The detailed results of these experiments will soon appear as No. 9, 

 Volume 3 of the " Publications of the Allegheny Observatory." On 

 this occasion it will suffice to give merely the results. 



A number of regions covering about twenty-five square degrees 

 each, were photographed in duplicate, first with the center of the 

 plate at the center of the region and then with the edge of the plate 

 in that position. A comparison of the two sets of positions gives 



o".i8 



as the probable error of the measurement of one image. This 

 quantity includes not only the accidental error but the following as 

 well: (i) outstanding errors in the measuring engine; (2) the optical 

 distortion of the objective, due to a possible failure of the objective 

 to give a truly linear reproduction of the object photographed; (3) 

 magnitude distortion due to spherical aberration and causing bright 

 stars to appear systematically nearer or systematically farther from 

 the center than faint stars. The result shows that all of these errors 

 are very small, and additional experiments indicate independently 

 that (2) and (3) are negligible or very nearly so. 



Doublets have been extensively used in astronomy for pictorial 

 purposes. The doublet that we have used for the above experi- 

 ments dififers in one important respect from these : the ratio of the 

 aperture to its focal length is twenty-one instead of five or six 

 This circumstance is favorable to its performance over a wide field 

 and is doubtless responsible for the smallness of the optical and the 

 magnitude distortions. 



Our objective covers well a field of twenty-five square degrees, 

 as compared with four square degrees in the case of the plates for 

 the Astrographic Catalogue. For the latter, as already stated, six 

 times as many comparison stars would be necessary in a large piece 

 of work in order to determine the plate constants equally well. The 

 scale of the astrographic plates is a little more than double that of 

 ours, and the purely accidental error of measurement is therefore 

 somewhat smaller, but not as much smaller as this difference in scale 

 would imply. In practice, so much of the accuracy of photographic 

 positions depends upon the comparison stars, that if a large area 



