STELLAR PHOTOGRAPHY. 



217 



TABLE V. 



The average values of these residuals, taken without regard to sign, are 0.087, 

 0.051, 0.051, 0.029, 0.044, 0.047, and 0.059, in the seven columns respectively. The 

 first of these values is decidedly greater, showing that it was difficult to set with 

 accuracy on the centre of so long a line as that produced when the exposure lasted 

 for two second.?. The Last value is also somewhat greater, owing to the difficulty of 

 determining the end of a trail. The difference is, however, much less than was 

 anticipated. The mean of all the residuals is 0.053, or, if we use only the intervals 

 between short exposures and reject the first and last values, 0.044. Since all of 

 these values are found from the difference of two settings, we must divide by the 

 square root of two to obtain the average deviation of a single setting. "We thus 

 obtain the values 0.037 and 0.031. The probable error of a single setting is found 

 by multiplying these values by 0.85, which gives ±0.031 and ±0.026. No setting 

 has been rejected for discordance, and no change made in the original record except 

 that the seventh setting on Maia was recorded 54.685 and was assumed to mean 

 54.635. This setting 54.685 would render the preceding and following values so 

 large that they would have to be rejected for discordance. One would be increased 

 and the other diminished by 0^70. As shown in the Table, the assumed value 

 gives the residuals +0'.04 and +0'.03. To show how far the deviations were due 

 to errors of setting, ten successive settings were made on a single image of Celaeno, 

 and gave an average deviation of iO'.OlS and a probable error of ±0'.013. These 

 various values could doubtless be reduced by the use of a higher magnifying power, 

 that employed being much too low. The probable error of a transit over a single 



