been from 3 to 6 minutes per annum and, on the far western coast, from 2 to 5, while the line of no variation persists fairly well in staying in one place. It is, therefore, part of the Survey's duty to record these eccentricities of the needle. As an important auxiliary to their detection, the Survey maintains a magnetic observatory in Vieques, an island lying to the east from Porto Rico; another in Maryland, a third in Arizona; one in Sitka, and one in the Hawaiian Islands. In all of these observations are made by continuous photographic registration. All the world is busy with similar observations, and whenever a scientifically equipped expedition, as for example the recent ones to the Antarctic, starts out, there is a general coöperation between the different governments of the world for the purpose of making simultaneous observations. It is to be hoped that sooner or later the mystery will be fathomed so that predictions of what is going to happen can be made.

The Triangulation and the Figure of the Earth.-In so extensive an undertaking as a trigonometric survey of the coasts and interior of our country it inevitably happened that surveys were made in detached localities, in Maine, in Florida, on the Gulf, and on the Pacific coast. Each area was referred to some local datum just as detached leveling would be. Gradually, these separate surveys were connected and it became necessary to adopt an origin of coördinates in reference to which all geographic positions should be expressed.

Every extended triangulation, whose determined positions and relative bearings are to be given, is developed on some adopted spheroid of reference. In the beginning Bessel's spheroid was used by the Survey. Later on the geographical positions were computed on Clarke's spheroid. An enormous amount of computation is involved in shifting from one to another and yet it is desirable to utilize all increase in knowledge of the size and figure of the earth.

In order to meet the difficulties presented by these conditions it was decided to separate the refined investigation of the figure and size of the earth from the practical requirements of using a spheroid, which should be sufficiently close for the practical requirements of the surveyor, the engineer, and the geographer. It is believed that the Clarke spheroid, of 1866, which was adopted by the Coast and Geodetic Survey, satisfies these latter requirements for the whole American Continent. The Survey next selected a particular point in the triangulation and a direction, and now, when triangulation is spoken of as being on United States Standard Datum, the meaning is that

the triangulation has been referred to Clarke's spheroid on which this particular point has a definite position.

Not only the Coast and Geodetic Survey triangulation, but that of the Lake Survey also, has been referred to this datum and wherever the topographic work of the Geological Survey has been connected with the triangulation of the Coast and Geodetic Survey it is equally referable to this datum. In this way has been achieved a homogeneous system of geographical coördinates for the vast domain of the United States, and it is not unlikely that Canada and Mexico will continue the same system.

It is not necessary to point out to engineers the practical value of a trigonometric survey. New uses for it continually arise. Witness the cadastral survey of Greater New York which is based on U. S. triangulation. The Oyster Surveys of the various States utilize the trigonometric points for the delimitation of the oyster-beds. The Coast Artillery is supplied with data which are used for fire control, and, in general, the network of triangulation forms a basis for coordinating all topographic and economic surveys, and thus the work accomplished is forever increasing in value and usefulness.

Among the unforeseen applications was the demonstration of the precise amount of the displacement of the earth's surface, by the San Francisco Earthquake along the fault line, and the extent of the movement at right angles to it.

Until about six years ago the method of deriving the figure and size of the earth from triangulation was to deduce it from measured arcs of parallels and meridians. That is, after the length of a meridional arc or parallel had been measured, the angle which its termini subtended was astronomically determined. But owing to the irregular distribution of masses on and within the earth's crust the actual direction of the Zenith differed from the geometrical Zenith of the spheroid of reference. This well-known error, called the deflection. of the plumb line, was assumed to average out in a large number of arc measurements. At any rate no correction for it was applied.

A great many years ago, Archdeacon Pratt, while studying the pendulum observations made in India, reached the conclusion that wherever there were visible mountain masses such as the Himalayas there was a corresponding defect of mass in the earth beneath, but it was reserved for the Coast and Geodetic Survey to extend and apply this theory in the computation of the size of the earth from are. measurements by introducing into Geodesy what is now known as

the principle of Isostasy. This principle is that the matter composing the earth's crust to a certain depth has a tendency to adjust itself to a condition of hydrostatic equilibrium or has done so. Stated in another way, upwards from a certain depth below sea-level, each unit area has the same amount of mass above it whether we measure to the summit of mountains or merely to sea-level.

By trial computations, the most probable depth to which this compensation extends, was found to be about 122 kilometers, or 75 miles. Note how the work of the geodesist trenches on the domain of the geologist and geophysicist.

The hypothesis of isostatic compensation having been introduced, the effect of the visible topography for a distance of about 2500 miles was computed for each of the primary triangulation stations of the Survey, and the deflection of the zenith, previously referred to, was corrected at each station. Then the spheroid, whose surface most nearly agreed with the surface of the United States, was deduced and this gave the corrections to Clarke's spheroid. It is safe to say that the values for the compression and semi-diameters of the earth, resulting from these computations, are the most accurate known. It may be added that, when the results of this work were presented two years ago to the International Geodetic Association in London, the Americans were congratulated on having made a new epoch in Geodesy.

The Pendulum.-While one must rely on trigonometric observations to determine the size of the earth its figure can be determined by gravity observations, that is, by the pendulum alone. It is, therefore, a very important auxiliary in a Geodetic Survey. For the purpose of comparison the observations made with the pendulum must be reduced to sea-level. The manner of reducing them is one of the moot questions in Geodesy. Now, the recognition of the existence of isostatic compensation, which has been proved by purely astronomic methods, compels one to take it into account in the pendulum reductions. The method of reduction just introduced in the Survey not only does that, but, also, for each station, takes into account the effect of the attraction of visible masses for the whole earth. This is a great stride in advance; but the inevitable logic of this process has not been received abroad with open-minded enthusiasm. The correctness of the method has been proved for gravity work in the United States, and it is for others to show that. it does not apply to the rest of the world.

The International Geodetic Association. To make a new epoch in science is no mean achievement; but mention has already been made of the compliment paid to the Americans at the last meeting of the association in London. This association exists by virtue of a formal convention between the great powers of the world. It is an official organization whose object is to promote knowledge of the size and figure of the earth. Canada, the United States, Mexico, and Argentina belong to it. So do Japan and, practically, all the powers of Europe. It is one of the oldest of international scientific associations. The delegates to the meetings report progress, and compare methods and results, and endeavor to strengthen such undertakings as the Cape to Cairo Arc of the Meridian and the junction of the Great Trigonometric Survey of India with the Russian Survey. To carry out this last piece of work the association covets the coöperation of China and hopes that that ancient empire will ultimately join the other powers in the undertaking.

Among the tasks undertaken by the association is the determination of the variation of latitude. For this purpose, it maintains six small observatories in the northern hemisphere, two of which are in this country and are under the direction of the Superintendent of the Coast and Geodetic Survey.

Two years ago the astronomer in charge of the Observatory at Gaithersburg, Md., proposed the construction of a Zenith tube for photographically determining the variation of latitude and, at the author's request, the association gave about $2500 for the purpose. The instrument was constructed in this country, has been mounted, and the preliminary results indicate that a step in advance has been taken by securing a higher degree of accuracy, than was before attainable, with a considerable simplification of methods.

The association meets once in three years and the principal countries in Europe have vied with each other in extending invitations for meeting in their capitals. Although the Coast and Geodetic Survey has taken an honorable part in these meetings it has never had the privilege of extending the hospitality of this country to the association. Mention of this fact is made with the same embarrassment that the author feels in representing a great nation at such meetings, and having to maintain silence when the different nations of Europe are competing for the place of meeting.

The Geodetic Level.-Fig. 2 shows a picture of the leveling instrument, developed in the Coast Survey, with which nearly all engineers

are familiar. The instrument may be called a binocular level because there is a telescopic attachment by means of which the level is read by the observer without shifting his position. The level bubble itself is set into the telescope tube so as to be near the line of sight. Furthermore, the telescope tube is made of the alloy of nickel and steel called "invar" which has a coefficient of expansion of only about one-tenth that of steel.

The introduction of this level has added greatly to the accuracy of

the operations, the speed with which the best grade of work can be done has been much increased, and the cost correspondingly reduced. In a slightly modified form it is in use in the Geological Survey. The Egyptian, Australian, and Canadian governments have also introduced it, and a recent report of the Director of the Great