On October 8th, 1867, at about half-past eleven in the evening, I noticed that Algol had reached its minimum of brilliancy. Hence the next minimum was attained at about a quarter-past eight on the evening of October 11th; the next at about five on the evening of October 14th, and so on. Now, if this process be carried on, it will be found that the next evening minimum occurred at about 10h. (_circiter_) on the evening of October 31st, the next at about 11h. 30m. on the evening of November 20th. Thus at whatever hour any minimum occurs, another occurs _six weeks and a day later_, at about the same hour. This would be exact enough if the period of variation were _exactly_ 2d. 20m. 48s., but the period is nearly a minute greater, and as there are fifteen periods in six weeks and a day, it results that there is a difference of about 13m. in the time at which the successive recurrences at nearly the same hour take place. Hence we are able to draw up the two following Tables, which will suffice to give all the minima conveniently observable during the next two years. Starting from a minimum at about 11h. 45m. on November 20th, 1867, and noticing that the next 43-day period (with the 13m. added) gives us an observation at midnight on January 2nd, 1868, and that successive periods would make the hour later yet, we take the minimum next after that of January 2nd, viz. that of January 5th, 1868, 8h. 48m., and taking 43-day periods (with 13m. added to each), we get the series-- h. m. Jan. 5, 1868, 8 45 P.M. Feb. 17, ----, 8 58 ---- Mar. 31, ----, 9 11 ---- May 13, ----, 9 24 ---- June 25, ----, 9 37 ---- Aug. 7, ----, 9 50 ---- Sept. 19, ----, 10 3 ---- Nov. 1 ----, 10 16 ---- Dec. 14, ----, 10 29 ---- Jan. 26, 1869, 10 42 ---- Mar. 10, ----, 10 25 ---- Mar. 13, ----, 7 43 ----[7] Apr. 25, ----, 7 56 ---- June 7, ----, 8 9 ---- July 20, ----, 8 22 ---- Sept. 1, ----, 8 35 ---- Oct. 14, ----, 8 48 ---- Nov. 26, ----, 9 1 ---- Jan. 8, 1870, 9 14 ---- Feb. 20, ----, 9 27 ---- From the minimum at about 10 P.M. on October 31st, 1867, we get in like manner the series-- h. m. Dec. 13, 1867, 10 13 P.M. Jan. 25, 1868, 10 26 ---- Mar. 8, ----, 10 39 ---- Apr. 20, ----, 10 52 ---- June 2, ----, 11 5 ---- June 5, ----, 7 53 ----[8] July 18, ----, 8 6 ---- Aug. 30, ----, 8 19 ---- Oct. 12, ----, 8 32 ---- Nov. 24, ----, 8 45 ---- Jan. 6, 1869, 8 58 ---- Feb. 18, ----, 9 11 ---- Apr. 2, ----, 9 24 ---- May 15, ----, 9 37 ---- June 27, ----, 9 50 ---- Aug. 9, ----, 10 3 ---- Sept. 21, ----, 10 16 ---- Nov. 3, ----, 10 29 ---- Dec. 16, ----, 10 42 ---- Jan. 28, 1870, 10 55 ----