The Rutherfurd Photographs. 273 



In the tabulation of results the probable error of each right as- 

 cension and declination is given. We may compute the prob- 

 able error of right ascension of a star as derived from a single 

 plate by the expression 



±0.6745^-^7^ cos (5 « 

 * 264 — 66 



where [vu] is the sum of the squares of all the residuals in right 

 ascension for the thirty-three stars which appear on all eight 

 plates ; the factor cos d Q serves to reduce the probable error to 

 arc of a great circle. The expression for the probable error of a 

 single declination is identical with the above except that cos d Q 

 is omitted. In this way we obtain the probable errors, 



In Right Ascension. In Declination. 



±o".o8i ±o // .058 



If we do not confine ourselves to the thirty-three stars as above, 

 but use all the stars, we get 



±o // .o8o ±o // .o6o 



Thus it appears that the uncertainty in a right ascension or in 

 a declination is considerably greater than that in the correspond- 

 ing measured coordinate. We may conclude from this that when a 

 large number of plates is available, better results will be attained, 

 for a given expenditure of time and labor, by measuring a large 

 number of plates rather than measuring a few with all the 

 elaboration used in the present research. But for the Ruther- 

 furd photographs such elaboration is amply justified by the very 

 limited number of existing photographs of so early a elate. 



It might appear at first as though a large part of the discrep- 

 ancy between the two sets of probable errors, namely, those for 

 the measured coordinates, and those for the resulting right ascen- 

 sion and declination, could be accounted for by the .uncertainty 

 of the constants used for the several plates. That such is not the 

 case appears from the following considerations : the residuals 

 for the five comparison stars, given on pages 247 and 248, 

 exhibit a remarkable uniformity, showing that the greater part 

 of these residuals is due to inaccuracies in the meridian observa- 

 tions. It follows, therefore, that the probable errors given for 

 the constants p, r, k and c, are due not so much to errors in 



