30 PROCEEDINGS OF THE AMERICAN ACADEMY 



plified by the fact that the apparent path of the satellite during the 

 eclipse is nearly rectilinear. It was found that, if tlie longitude of 

 the line of nodes was made equal to 17°, the periods of ingress and 

 egress would be nearly equal. The peri-astron then happens to coincide 

 with the point of egress. The variation in light due to tliis orbit is 

 compared with observation in Table XI. The successive columns 

 give the time, the observed light in grades, the logarithm of this light, 

 and its value compared with the full light of the s^tar. The next col- 

 umn gives the light already found in the second column of the second 

 part of Table X., and which may be called A. The next column 

 gives the variation in light for the elliptical orbit assumed above, which 

 will be denoted as B. The second part of the table gives the residuals 

 found by subtracting these values of the light from those observed. 

 The last columns give the residuals found by subtracting the logarithms 

 of these quantities. Although the residuals even of A are not very 

 large, they are systematic, being positive when the light diminishes, 

 flnd negative when it increases. The residuals B are much smaller 

 than those of A during ingress, but they are larger during egress. 

 In other words, while the systematic error of ingress has been nearly 

 eliminated, a nearly equal error has been introduced during egress. 

 Accordingly the average residual is not diminished. We have so 

 far adopted the times of first and last contact given by Schon- 

 feld. An inspection of the table from which he derived his curve 

 shows that the weight he assigns to his observations when more than 

 three hours from the minimum is small, and that consequently the 

 times of contact must be somewhat uncertain. The exact time of 

 minimum must also be uncertain, although to a less d'-gree than that 

 of the two points just mentioned. An approximate solution by least; 

 squares was therefore made, with the times of contact and of minimum 

 as unknown quantities. One half weight was given to the equations of 

 condition formed from the observed terms of contact. From this a 

 correction to the observed minimum was found of 5 minutes, or the 

 true minimum appears to occur nearly one tenth of an hour later than 

 that given by the curve. The time of first contact should also be 

 diminished by about 2 minutes, and the time of last contact increased 

 by about 13 minutes. The columns (7 give the values of the light and 

 of the residuals corresponding to this orbit. The third j)lace of deci- 

 ma's is not always exact, as tliis would have involved a great increase 

 in the labor of computation and the accuracy attained appears to be 

 all tliat is at present justified by the observations. 



The residuals thus obtained are quite satisfactory as regards their 



