future career, are clearly laid down, and under each rule examples are given. The organs of the day expressed their opinions in terms of the highest eulogy. The _Liverpool Mail_ said, “Mrs. Taylor indeed merits high praise, and we add national gratitude; she has removed the chief difficulties which obscured the science of navigation. We have no hesitation in saying, that here is the most complete treatise on navigation which has ever been published.” In 1854, the seventh edition of “Lunar and Horary Tables: with the shortest method of finding the Longitude and the Time,” appeared. This work was highly recommended by gentlemen well qualified to test its merits, and who could not be affected by mere partialities. It gives a very simple, easy, and accurate method of working the lunar problem. These learned and laudable volumes were deposited in the library of the Vatican, in 1860. The above are not all the writings of Mrs. Taylor, but they are amply sufficient to prove that she was a mathematician of the first class. Her logarithmic tables are correct and complete in no ordinary degree. Such rare knowledge she did not gain from merely attending lectures on the various subjects which her own taste led her to cultivate, or which fell within her reach. Neither did she furnish her mind by the mere reading of books. In both ways, or in either, it is true, much information may be acquired; but still it may be knowledge only imposed upon the mind, not received within it. Knowledge, to be useful, must be attained by young and old, through an exercise of the reasoning power which very quickly leads to a conviction that the learner is treading upon firm ground. Between a woman who tests and tries every opinion and principle subjected to her notice, and one who does not, there are no points of comparison; the one may adopt false sentiments, but the other cannot be said to have any sentiments at all, only a collection of prejudices and predilections in their place. _NAUTICAL AND MATHEMATICAL ACADEMY._