266 Permanence of the Rutherfurd Photographic Plates. 



It is clear that if we had been able to turn the plate exactly 90° 

 each time, all the above readings of minutes and seconds would 

 have been exactly equal to the mean given at the foot of the 

 column. If we let : 



^ + * be the mean of all the readings, omitting the degrees, 

 Q be the reading actually obtained in any case, 



then i will be the correction required by the reading actually 

 obtained, to reduce it to what it should have been. In some 

 cases it was more convenient to use as the standard reading to 

 which the actual readings are to be reduced, some number which 

 was nearly equal to the majority of the readings instead of the 

 arithmetical mean of all. In this way i was generally made 

 quite small. 



Having obtained the value of i, we can proceed to the correc- 

 tion of the measured coordinates. Let : 



a;,,ys,x/,y/, be the coordinates obtained for the two standard 

 stars in the special measures made for the purpose of 

 getting a uniform scale value for both coordinates. 



ar, y, x% y', be the corresponding coordinates of the same standard 

 stars in any set of measures. 



it, ij be the values of i belonging to the special standard measures 

 and the other set of measures. 



To get the true distance between the standard stars parallel 

 to the X and ?/-axes, we must correct the ones obtained directly 

 from the special standard measures by adding : 



to Xs — x/, the quantity — {ys — ys') is sin 1^^ 

 to ys — ys', the quantity + {xs — Xs') is sin i'^ 



In making these special standard measures in two coordinates the 

 greatest care was taken to insure the complete elimination of 

 temperature effects by using the principle of repetition in the re- 

 verse order, and by making all the measures in a consecutive 

 series on one day. Consequently, we may assume that the cor- 

 rected Xs — x/ and y^ — y/ are measured at the same tempera- 

 ture, and are, therefore, expressed in the same unit of measure. 

 This unit of measure is of course the mean millimetre of the scale 

 at the mean temperature of the day on which the special standard 



