OF ARTS AND SCIENCES. 379 



the minimum, it is diiRi'iilt to uiulerstand what instrumental errors 

 could have caused the deviation. Inchiding this minimum, the mean 

 deviation for the seven nights is 5.2 minutes, or excluding the obser- 

 vations of Nov. 22, 3.2 minutes, the corresponding probable error 

 would equal 4.7 and 3.0 minutes. The mean of the probable errors 

 given in the next column is 3.8 minutes. This compares favorably 

 with the results of naked-eye observations. Schmidt * gives tlie prob- 

 able error of a single minimum observed by Argelander to be G.O 

 minutes ; of those of Schonfeld, 4.6 minutes ; and of those by himself, 

 8.0 minutes. Probably still better results could have been obtained 

 photometrically had the observations been designed for determining 

 the time of minima. The mean of the whole series of measures would 

 imply a correction to the adopted curve of -)- 1.8 minutes, with a 

 probable error of 1.3 minutes. But if the observations of Nov. 22 are 

 rejected, the correction becomes — 1.6 minutes. It therefore seems 

 better to retain the correction to the ephemeris of 37 minutes, already 

 adopted. 



We have now a means of determining more precisely the constant 

 difference between the different observers. The differences so far as- 

 sumed are, P = 0.00, S = — 0.22, and W =r 0.00 magnitudes. If 

 either observer had taken an equal number of observations before and 

 after the minimum, — or more strictly, if the weight of his observa- 

 tions before and after the minimum were equal, — an error in this 

 correction would not affect the result. It would, however, very slightly 

 exaggerate the residuals, and consequently the probable errors. If 

 these personal differences were zero, the algebraic sum of the residuals 

 of each observer should be zero. In fact, their values for the three ob- 

 servers are, for P = — 2.43, for S = -}- 1.66, and for W = -|- 1.84. 

 As the total number of sets in the three cases are 98, 57, and 64, we 

 obtain by division the deviations — 0.02, -|- 0.03, and -j- 0.03. Com- 

 bining with these the correction of 0.22 already derived from Mr. 

 Searle's observations of the full light of the variable, we find that 

 the correction required to reduce his measures to mine is -)- 0.17, and 

 to reduce Mr. Wendell's — 0.05, magnitudes. The effect of these 

 changes on the final result would probably be wholly insensible. 



Line 14 of the above table shows clearly that the observations of 

 Nov. 19 should be rejected. They would indicate an error of an hour 

 and a half in the minimum, if the deviations were not so large that the 

 present method could not be applied. 



* Astron. Nach.. Ixxxvii. 204. 



