OP ARTS AND SCIENCES. 395 



All of the observations are compared in Table XIV. Tlie columns 

 give a current number, E or the number of minima which have 

 elapsed since the discovery of the variability, the date, hour, and 

 minute according to the approximate epliemeris used, and the ob- 

 served minimum in mean time of the meridian of the observatory 

 named in the fifth column. The last two columns give the correc- 

 tion to the ei)hemeris and the name of the observer. Observations 

 made at the Harvard College Observatory are designated by II. C. O. 

 Schmidt I. and Schmidt II. denote the two reductions referred to 

 above. 



For comparison with different ephemerides it will be convenient 

 to group the observations of each observer, as has been done in 

 Table XV. The observations of Dr. Schmidt in August according 

 to his first and second reduction have been placed together, and also 

 his later observations. The successive columns give a current num- 

 ber, the authority, the number of minima observed, and the mean 

 value of E. The last four columns give the corrections in minutes to 

 be applied to four ephemerides ; that is, they equal the mean of the 

 observed minus the computed value of each group according to the 

 following four formulas : — 



(A) Ep. E. = 1880 June 23'J 7" 44.0'" -f 2* IP 50.0 " E. 



(B) Ep. E. = 1880 June 23* 10" IS.l-" + 2^ 11'' 44.94" E. -4- 0.04376"' E^. 



(C) Ep. E. = 1880 June 23-i 8" 12.0"' + 2* 11" 49.6"' E. 



(D) Ep. E. = 1880 June 231 71, 41 q"' -j- 2* 11" 49.9'° E. 



The first of these formulas (A) is extremely convenient, since the 

 minutes repeat themselves every six minima. As the period differs 

 from two days and a half by exactly ten minutes, the times of the suc- 

 cessive minima may be written down directly. Every two hundred 

 and forty minima, or every five hundred and ninety-nine days, the 

 hours and minutes repeat themselves, so that the ephemeris can be 

 easily extended over long periods. Whatever ephemeris is adopted, 

 it may be more convenient to compute the minima by this formula 

 first and apply the difference of the ephemerides as a correction. 



Formula (B) is derived from the law proposed by Dr. Schmidt on 

 page 90 of his article, reducing to Paris mean time and adopting 

 June 23 as the starting-point, as in the other ephemerides. A mini- 

 mum is assumed to have occurred on December 7 at 1 0'' 6.7™, Athens 

 mean time. The period at this time is taken as 2*^ 11'' 50.812™, with 

 an increase of 0.08753 in each successive period.' The ephemeris on 

 page 91 is nearly, but not exactly, represented by this law. A part 



