selected. The chief difficulty, however, was in joining the ends of various lines, each referred to separate points.
The author personally visited many of these terminal points, and had new determinations made when necessary. That he has succeeded may be seen from his results for the altitude of Denver, derived from the lines of the Kansas Pacific and Union Pacific Railroads. This altitude is 5,198.97 feet by the Kansas Pacific Railroad surveys, and 5,194.20 feet by the Union Pacific Railroad surveys, a difference of less than five feet in lines nearly 2,000 miles long, which were run at different times, by many different engineers.
In the eastern part of the United States there are many opportunities to check such results in places situated on two or more roads, and the examination of a few such checks will serve to give an idea of the agreement to be expected. At Harrisburg, for example, we have two lines of level, one brought by the Coast Survey and the Pennsylvania Railroad from Raritan Bay (175 miles), and the other from Baltimore by the Northern Central Railroad. The first gives 319.91 feet, the second 319.75. Tin's agreement is rather closer than could be expected, and, although the author does not mention it in this connection, it is subject to an uncertainty in the determination of mean tide at Baltimore, noted further on.
The height of the Chicago city directrix above mean tide, as determined by the surveys of the Pennsylvania Railroad and its connections (900 miles), is 585.41 feet; from the surveys of the New York Central Railroad and connections 587.57, and this agreement is perhaps a fair type of what we may expect from surveys conducted with care over long-established railway-lines.
We will adduce one more example, determining the elevation of the mean surface of Lake Erie: the independent results are 573.08, 572.04, 572.67, 570.75, 571.67, and [581.20]. The last determination is rejected on the testimony of the chief-engineer of the railroad from whose surveys it is given.
Mr. Gardner states, as the results of his experience, that most of the errors found are produced by hasty computation and careless combination of results, rather than by imperfect instrumental work. This is shown by his own careful combinations to be the case, since we cannot consider the agreement he has found as fortuitous. He recommends civil-engineers to connect their surveys with the city-directrices and to send a copy of their profiles to the Signal-Office in Washington, so that their careful work may be made of scientific use, by suitable discussion.
As the results of this investigation Mr. Gardner announces that the great lakes and the surrounding country are now recorded 9 feet too low St. Louis 23 feet too low, Kansas City 100 feet too low, Indianapolis 100 feet too low, and Omaha 31 feet too low.
These corrections rest on various data, and are not all of equal certainty, but they must be accepted for the present. The whole subject must eventually be thoroughly discussed; until it is, this valuable research will be the standard.
Polarization of Light. By William Spottiswoode, M. A., F. R. S., etc. New York: Macmillan, 137 pp. Price $1.00.
The diffusion of Prof. Tyndall's "Lectures on Light" in tens of thousands of copies throughout the United States has awakened a popular interest in even the more abstruse questions connected with that topic. Mr. Spottiswoode's little volume is devoted to the phenomena of polarization, which it discusses in a style adapted for popular comprehension. The method of the book is synthetic—the phenomena of polarization and its different processes are first brought before the mind of the reader in a number of experiments (which are fully illustrated); then the author explains what is meant by the undulatory theory of light. The phenomena of polarization are seen to accommodate themselves so thoroughly to this theory, that a simple approximation of the two is sufficient to prove that the one is the law of the other. Having thus coördinated the phenomena, the author considers in separate chapters "Circular Polarization," "Phenomena produced by Mechanical Means," "Atmospheric and other Polarization," "Figures produced by Crystal Plates," and "Composition of Colors by Polarized Light." The subject last named is illustrated by means of two very beautiful chromo-lithograph plates.
