This work remains one of the most profound efforts of mathematical research on record. Bowditch’s accuracy has passed into a proverb. He gave the latitude of all the principal seaports of the world with marked precision; while some of the longitudes are now found to be slightly in error, it is surprising that his determinations of those of Boston and Philadelphia should be exactly the same as those obtained by the best methods in use to-day. But he makes San Francisco and Halifax seven miles too far to the east, and New York eight miles too far west. But we are to remember that for this computation the best available instruments were the chronometers of a century ago, and that lunar observations were made with the old-time sextant. [Illustration: ZENITH TELESCOPE. Made for University of Pennsylvania by Warner & Swasey.] As applied to geodesy, astronomy has added a process of ascertaining geographical latitude with marvelous accuracy and speed by the use of the zenith telescope, an instrument devised by Major Talcott in 1835. This instrument can be set in a vertical direction with ease, and be pointed alternately to two stars that cross the meridian at a brief interval of time, the one north and the other south of the zenith. Difficulties that arise from refraction are avoided, and the resulting latitude is quickly computed. This method is largely employed in the surveys of the public lands, as also in establishing the boundary between the United States and British America. XIV. NOTABLE EPOCHS IN THE NINETEENTH CENTURY. Worth marking as epochs of the nineteenth century were such dates as October 10, 1846, when the first determination of difference of longitude of two places was made by the use of the telegraph wire. Sears C. Walker, in Washington, and E. Otis Kendall, in Philadelphia, compared their clocks by interchanging telegraphic signals, and thus found their respective longitudes. In 1850, Professor William C. Bond, of Harvard College, invented the chronograph. Through the urgency of Sir David Brewster, it was shown in the great exhibition of that year in London, where a medal was awarded for it. The chronograph was speedily adopted throughout Europe, and together with other apparatus made by Bond constituted what there became known as the “American method” of recording observations. Through it the errors for which the “personal equation” is a partial remedy are largely eliminated, and a superior definiteness of record is obtained.