346 H. Jacoby — Determination of the Division 



which does not differ very much from the weight obtained in 

 method 1. 



6. As an example of the use of method 1, I have caused two 

 of my students, Messrs. Schlesinger and Ling, to make a deter- 

 mination of the non-periodic errors of one of the screws of 

 the double microscope of the Repsold machine for measuring 

 photographs at Columbia College Observatory. The method 

 is admirably adapted for this purpose, and 1 am not aware that 

 it has been used elsewhere for examining screws. It is merely 

 necessary to take readings on the successive divisions of the 

 millimeter scale of the machine, arranging them in accord with 

 the scheme explained above. Such a set of readings is set 

 down in Table A below, the number attached to each screw- 

 reading being the weight of that reading, or the number of 

 times the line of the scale was bisected at that point. The 

 exterior quantities have been observed three times, instead of 

 four, as recommended in this paper. This was done to save 

 time. Table B is obtained from Table A by taking the dif- 

 ferences of the successive numbers, and corresponds exactly to 

 Table I given on page 336. In Table C the K's are set down, 

 and their summation gives the corrections of the screw at the 

 points 5, 7, 9, 11, 13, 15, revolutions. In column four of 

 the table the necessary corrections are applied to give results 

 in terms of the screw as a standard, instead of the scale. This 

 is done by means of equation (1). Column five contains the 

 corrected division errors, as determined by the observer S. 

 Columns six and seven contain the results of the observations 

 by L. and of a second set of observations by S. The last 

 column gives the mean. In all these tables, unity in the fourth 

 decimal place corresponds to one-twentieth of a micron on the 

 scale. It will be noticed that in one case only does the differ- 

 ence from the mean amount to half a micron, or -%-§\-%-§ of an 

 inch on the scale. This implies that in measuring any object 

 with this microscope, we need not fear errors of greater amount 

 than -g-o-Jiro- inch, on account of the non-periodic errors of the 

 screw. It is to be noted also that this method gives the errors 

 of the screw without the assumption of any law of error, 

 while in many investigations by other methods it has been 

 customary to assume that the non-periodic screw errors could be 

 represented by a parabolic curve. 



