algebra and mathematical formulæ for calculations and reductions she had to gather when and how she could: chiefly at meals, and at any odd moments when her brother could be asked questions, and the answers were carefully entered in her Commonplace Book, where examples of taking equal altitudes, and how to convert sidereal time into mean time, follow upon pages of problems, oblique plain triangles, right-angled spherical triangles, how to find the logarithm of a number given, and theorems for making tables of motion. With this slender store of attainment she accomplished a vast amount of valuable work, besides the regular duties of assistant to so indefatigable an observer as Sir William Herschel. He was invariably accustomed to carry on his telescopic observations till daybreak, circumstances permitting, without any regard to season; it was the business of his assistant to note the clocks and to write down the observations from his dictation as they were made. Subsequently she assisted in the laborious numerical calculations and reductions, so that it was only during his absences from home, or when any other interruption of his regular course of observation occurred, that she was able to devote herself to the Newtonian sweeper, which she used to such good purpose. Besides the eight comets discovered by her, she detected several remarkable nebulæ and clusters of stars previously unnoticed, especially the superb nebula known as No. 1, Class V., in Sir William Herschel’s Catalogue. Long practice taught her to make light of her work. “An observer at your twenty-foot when sweeping,” she wrote many years after, “wants nothing but a being who _can_ and _will_ execute his commands with the quickness of lightning; for you will have seen that in many sweeps six or twice six objects have been secured and described in one minute of time.”