Fermanence of the Rutherfurd Photographic Plates. 199 



the improved machine. But in the case of the present research, 

 the omission of these errors is of minor importance, for it is not 

 our object to obtain the coordinates of the stars with the verj'" 

 last degree of precision possible. It is only intended to get a 

 comparison of the old and new measures, and it is evident that 

 the omission of these tiny corrections will tend to diminish the 

 agreement of the two sets of measures, if indeed it has any ap- 

 preciable effect at all. Consequently the favorable conclusion 

 which we shall obtain further on as to the durability of the 

 Rutherfurd plates will not be impaired in the slightest by the 

 circumstance that we have omitted these errors of projection. 



We shall now consider the above different errors of the measur- 

 ing machine, beginning with the errors of the micrometer screw. 

 The periodic errors of the screw were not determined, because it 

 has always been possible to eliminate them almost completely by 

 repeating all measures with the position of the screw changed by 

 half a revolution. The non-periodic, or progressive errors were 

 •determined by a modification of the method used by Gill for the 

 determination of the errors of the scales of the Cape heliometer. 

 I am not aware that this method has been used elsewhere for the 

 investigation of micrometer screws, and as it gives a determina- 

 tion of the progressive errors with very high precision but com- 

 paratively little labor, a brief description of it will not be out of 

 place here. The full description of the method in all its details 

 is now in course of publication in the American Journal of Science. 

 It can be applied directly to the screws of micrometer micro- 

 scopes, such as are used for reading scales or circles. 



The observations consist in a series of readings of the divisions 

 of the scale, taken with the micrometer microscope. In the pre- 

 sent case, the scale is divided into millimetres, and as two revolu- 

 tions of the screw correspond to one millimetre on the scale, it 

 has only been possible to determine the error of the screw for 

 each second complete revolution. A special scale a few milli- 

 metres in length, and divided into quarter millimetres, has been 

 made by the Messrs. Repsold, With this scale the non-periodic 

 errors will now be determined for a larger number of points on the 

 screws. 



The microscope is provided with an apparatus for counting the 

 whole revolutions of the screw, and the range is from 



K E 



5.0 to 15.0. 



