Permanence of the Rutherfurd Photographic Plates. 209 



N be one of the observed numbers in the table. 

 S be the corresponding reading of the scale, 

 a?, y be two constants to be determined. 



From each observed number in the table an equation of the fol- 

 lowing form was written down : 



From a solution of these equations by least squares the values 

 of X and y were determined. A separate solution was made for 

 each column of observed numbers in the preceding table. If we 

 then let: 



N' be the corrected value of the error of the cylinder, we can 

 compute N' by the equation : 



N' =^ N -^ k {S-265) X ^- y. 



It is evident that this method of reduction amounts to nothing 

 more than the application to the observed numbers of a correc- 

 tion that varies uniformly as we move along the cylinder. Such 

 a correction evidently removes the effect of any want of paral- 

 lelism of the cylinder and spider thread. The constant correction 

 y is added for convenience merely. 



The solutions of the equations by least squares give the fol- 

 lowing results : 



Observer Davis, Spider line direct, 

 Observer Davis, Spider line rever'd., 

 Observer Jacoby, Spider line direct, 

 Observer Jacoby, Spider line rever'd., 



Applying these numbers to the calculation of the corrected 

 errors of the cylinder, which we have called iV', we get the final 

 results contained in the following table : 



■ X 



y 



—0.000135 



—9.4985 



— .000188 



— -4953 



— .000260 



— .4981 



— .000089 



— .4984 



