OF ARTS AND SCIENCES. 373 



ance *liat the entire reduction has been repeated, rejecting them. No 

 exphination can be oflfered for this difference, which occurs in nine 

 sufficiently accordant sets. As the alternate observations of Mr. 

 Wendell on the same evening agreed with the results of the other 

 evenings, the effect seems to be due to the observer, and not to a vari- 

 ation of the star. The remaining observations have been arranged in 

 groups according to the time preceding or following the minimum. 

 Each grou]! extends over half an hour, the computed minimum being 

 the middle of one group. The first and last group extend from 255 

 to 345, the observations being more scattering. The results derived 

 from these groups are given in Table I. The first column gives the 

 mean of the times before or after the computed minimum. The latter 

 was taken from the Annuaire of the Bureau des Longitudes, 1880, 

 p. 78, which depends on the formula given by Schonfeld,* Ep. E = 

 1867 Jan. Qi lli^ 1.2'" M Z Paris + 2^ 20^ 48.9"' (E — 8534). 



The second column gives the number of sets in each grou[); and the 

 third the mean of the observed magnitudes. The points defined by 

 these times and magnitudes were then plotted on rectangular paper, 

 and a smooth curve drawn nearly through them. Various precautions 

 were taken to avoid small irregularities in this curve. The ordinates 

 were read off, and the residuals computed from straight lines nearly 

 tangent to the curve. These were plotted in turn, and the smooth 

 curve drawn through them served to correct the original curve. The 

 discussion of the rate of change in the light and of the true time of 

 minimum, given below, also furnished small corrections, so that the 

 curve should not only pass nearly through the observed points, but 

 i^hould undergo no sudden change in its direction or curvature. The 

 ordinates of the final curve are given in the fourth column, and the 

 deviations of the observations from them in the fifth column. 



An inspection of this table shows that the observed minimum pre- 

 cedes that given by computation by more than half an hour. To 

 determine the exact time of minimum, we must find the mean of the 

 times when the light is equal. If the light curve was symmetrical, 

 each of these means would equal the true minimum. Suppose that 

 points are constructed with abscissas equal to the mean times, and 

 ordinates to the corresponding light. Suppose that a smootli curve is 

 drawn through these points, and extended to the point whose ordinate 

 equals the light at the minimum. The abscissa of this point will give 



* Seclisunddreissigster Jahresbericht des Mannlieimer Vereins fiir Natur- 

 kunde, p. 94. 



