Page:The American Cyclopædia (1879) Volume IV.djvu/778

762 COAST SURVEY the water is produced by the joint attraction of the sun and moon, the height will be great- est, of course, when those bodies are in con- junction, that is, at new and full moon, giving rise to what mariners call spring tides. When the moon is 90 distant from the sun, or in quadratures, the joint effect will be least, and the neap tides will be produced. The discus- sion of this problem has engaged the attention of the most profound mathematicians since the days of Newton, particularly Laplace ; and yet the mathematical theories, although correct, have failed until recently in giving results which have been confirmed by observations. The cause of the discrepancies has existed, not in the mathematical deductions, but in a want of knowledge of the physical geography of the globe, and of the depth and form of the bottom of the sea ; and, although very important ad- vances in our knowledge of this subject have been recently made by scientific men both at home and abroad, yet it may be said that it is still one of the most perplexing questions in physical science. Prof. Bache, on assuming charge of the coast survey, organized a system of tidal observations, embracing the entire coast. It is the most extended system of ob- servations that has yet been 'attempted, and has already produced highly useful results. Of these the most important to mariners ia the publication annually by the const survey of a series of tide tables, by which they are en- abled to predict with great accuracy the time and approximate height of the tides at any of our more important harbors for every day in the year. This useful publication has now been in existence for several years, and its ad- vantages to the sailor are almost incalculable. Tidal observers in the coast survey service are required to note hourly the height of the water at each tidal station, by means of a staff placed in the water, by which also the precise times and height of high and low water can be de- termined. A self-registering machine is also much used, which, through the medium of clockwork, traces a curve on paper represent- ing the successive changes in the height of the water. More than 900 tidal stations have been established on the Atlantic coast ; and on the western coast observations have been made at frequent intervals for a distance of about 1,500 miles. The observations at the principal stations are continued through several years. Their investigation of course involves very la- borious computations ; the great object being to combine their results with theory, in such a manner as to furnish rules for the prediction of future results. The results of this branch of investigation in the survey have been published in the annual reports of the superintendent as the work has proceeded, showing the success which has attended the operation of the sys- tem. The report for 1856 contains tables of comparison of predicted tides of Boston harbor with the results of actual observation, in which the predicted times of high water coincide with the times observed within four minutes. Such accurate results had never before been ob- tained ; and this contribution to knowledge may be regarded as one of the most important of the present day. In the published tables we have the predictions of the height and times of high and low water for over 250 points on the At- lantic coast. On the Pacific coast predictions have been made with equal success for a great number of stations, and these are annually in- creasing in number. Prof. William Ferrel has developed a new method of calculating tides, of a purely dynamical kind. The method hitherto in use has consisted in supposing the water to be in a state of equilibrium under the attractions of the earth, moon, and sun, and then applying purely empirical corrections to the results so obtained. Prof. Ferrel has taken account of the fact that the water is in motion and has momentum. This was first done by Laplace, but unsuccessfully, because friction was neglected. Ferrel has taken ac- count of this. His theory has been applied by himself, at the desire of the present superin- tendent of the coast survey, to the case of Bos- ton harbor ; and its superior accuracy has thus been demonstrated, as well as its great value in saving laborious calculations of empirical corrections. Prof. Peirce has given much study to the calculation of the effects of fric- tion on tidal currents; and his results, com- bined with the original observations and re- searches of Mr. H. Mitchell, have produced a great advance in the theory of this subject, and important practical rules for draining tide lands, &c. Figure of the Earth. The geodetic system of surveying originated in the efforts of philosophers to determine the precise figure and size of the earth. It is well known that the earth is not exactly spherical in shape, but is flattened slightly at the poles of the axis about which it revolves, this axis being about 26 miles shorter than the equatorial axis. The determination of the relative lengths of the earth's axes has been one of the most impor- tant physical problems of all ages. The di- mensions of the earth are of course essential elements in the mathematical investigations connected with astronomy, and in the compu- tations of trigonometrical surveys. The mea- surement of extended arcs of meridian and parallel furnish the best means of determining these lengths ; and the problem has been con- sidered of so much importance, that expensive expeditions have been fitted out, and surveys made in different parts of the world, for this object alone. But, although approximate de- terminations have been made, it cannot be said that the dimensions of the earth are definitely settled. The primary triangulation of the coast survey furnishes incidentally val- uable contributions to science in this respect. An arc of the meridian 1,500 m. in length has been measured in India, one of 1,800 m. through Russia, extending from the Black sea to the Arctic ocean, and another of 900 m. in France,