March 17, 1905.] 



SCIENCE. 



411 



behind, its proper position, the stellar im- 

 ages will be elongated into lines having a 

 length dependent upon the amount of the 

 oscillation. If the telescope follows the 

 star only at one extremity of the oscilla- 

 tion, we shall have a series of images sepa- 

 rated by trails, or, if the rate of the tele- 

 scope is changed more, we shall have a trail 

 with dark knots appearing at regular inter- 

 vals. The number of the knots determines 

 the frequency of the oscillation, and almost 

 invariably indicates the driving-worm or 

 endless screw as the offending member. 



Such a periodic error, as shown by slide 

 1, is present in nearly all telescopes driven 

 in tliis manner. This fact is not anything 

 new, but has been recognized for years. 

 The first example that I know of personally 

 occnvred in 1888 with the Boy den thirteen- 

 inch telescope. In 1896 the director 

 asked me to determine the periodic error 

 of two of our photographic telescopes. 

 Several series o,f measures were made of 

 the eight-inch and the eleven-inch Draper 

 telescopes. The method was to view a 

 point of the tail-piece through a fixed mi- 

 croscope fitted with a micrometer. After 

 each release of the detent by means of the 

 signals given by hand, the position of the 

 point was read and recorded. The reduc- 

 tion of these measures shows that the oscil- 

 lation for the eight-inch Draper telescope 

 was about 1 second, and for the eleven-inch 

 Draper telescope about 0.2 second. These 

 figures correspond to trails of less than 

 0.01 cm. on the plate. Within a few years 

 Dr. Ilartman has studied the periodic 

 error of the Potsdam refractor and pro- 

 vided a very ingenious method of correc- 

 tion. A full account of his work will be 

 found in the Astronomische Nachrichten, 

 No. 3.769, page 2. 



Nothing further was done here until the 

 present year, when one of the small 

 cameras was provided with a new mount- 

 ing. The images proved to be lines lying in 



the direction of the clock's motion, and 

 might, therefore, be affected by a periodic 

 error. I proceeded to investigate the dif- 

 ficulty by a photographic method. The 

 polar axis of the instrument was displaced 

 in azimuth by a large amount. Such a 

 displacement would cause equatorial stars, 

 particularly when near the meridian, to 

 move over the plate in declination. If 

 an oscillation occurred, it would appear in 

 the sinuous character of the trail. Slide 

 2, which is enlarged ten times from the 

 original plate, shows the result, permit- 

 ting no doubt as to the nature of the error. 

 The numerous elongated objects are im- 

 ages of stars obtained on the same plate in 

 the ordinary way. It is seen that the 

 elongation of the images corresponds to 

 the amplitude of the oscillation as exhibited 

 by the vertical trail. The number of the 

 oscillations was fifteen per hour, which 

 fixes the responsibility upon the worm. A 

 similar experiment made with a worm 

 which had given satisfactory images is 

 shown in slide 3. A slight irregularity is 

 seen, but does not prove injurious. The 

 same experiment made with the eleven-inch 

 Draper telescope did not show anything 

 definite, due probably to the smallness of 

 the error. It is possible that it could be 

 brought out by attaching an enlarging ap- 

 paratus to the instrument and this will be 

 tried soon. 



The defective worm and several others 

 were also tested visually. A telescope of 

 about four feet focal length and having 

 an eye-piece provided with a crosswire, 

 was lashed to the camera and directed 

 to a scale graduated to millimeters and 

 placed at a distance. I was thus able 

 to record the position of the telescope ac- 

 curately. After every ten beats given by 

 hand to the driving mechanism, the posi- 

 tion was read for a period covering more 

 than a revolution of the worm, which oc- 

 curred in 240 seconds. The readings at 



