spans the boundary and the topographic mapping of a strip about two miles wide on each side of it. Aside from the immediate purpose of the delimitation, this work will serve as an admirable basis for co

ordinating the land and economic surveys which will follow in another generation or two.

Fig. 5 shows the southern limit of the work which has been accomplished. It is only a provisional limit for it will be necessary to go about 90 miles farther south, through the mountainous ice field

which lies to the north of Mount St. Elias. Just what can be accomplished there remains to be seen for it is plainly useless to plant monuments on moving glaciers.

Toward the north, in the land of the Midnight Sun, the transit line has crossed a range of mountains whose crests are estimated to be about 7000 feet high, distant about 20 miles from the coast. The last station is about 7 miles from the Arctic Ocean. The topography, triangulation, and monumenting have not been finished quite so far, and the details of this work are not yet at hand, as the parties are only just returning after a very successful season. The season was marred only by an outbreak of smallpox among the Indians which, as a matter of self-protection as well as for humanitarian reasons, engrossed the care and attention of the American Chief Engineer and his surgeon all summer.

The Survey is giving special attention to the publications, for the use of engineers, of the geographic coördinates, the descriptions of the trigonometric stations, and the leveling and magnetic results. The daily mail at the Survey office impresses one with the widespread and increasing demand for this information, and taxes the ability of the office to keep pace with it. Each division is in charge of an expert and the result is that the methods of the Survey compel the close attention and study of other nations and often serve as a model for them.

DISCUSSION.

M. B. SNYDER (visitor).—This seems to be a case where it is hardly possible to see the woods for the trees. The details which the head of the Geodetic Survey has been reviewing for us appear too manifold for just discussion, and it is almost impossible for us to comprehend the vast magnitude of the work of the Survey.

I think it is desirable to look at the woods, that is, to look at the great results which have been accomplished by this American institution, and to keep in mind that there is a possibility even in America, with all the difficulties with which we have to contend, of developing genuine science in governmental institutions. I have had a little experience in attempting to get the interest of Congressmen and Senators in a scientific subject, particularly in our enterprise of the Electrical Congress of 1884, and only those who have made such attempts can appreciate what the efforts mean. I think that as Americans we ought to sympathize with one another in the difficulties which all of us face in doing any scientific work, in the American atmosphere, and particularly sympathize with those who are trying to develop science in connection with governmental enterprise. I know that all who are attempting to do scientific work throughout the country

are looking with great interest toward those who are trying to develop in governmental institutions the strong scientific features which will tend to make our American civilization stable.

Professor Tittmann has been giving a brief account of the vast enterprises over which he presides, and I think we should extend our sympathy, and at the same time our hearty congratulations to him and his co-workers for such high effort toward making the United States notable, not for its "spread-eagleism,” but for its scientific enterprise.

E. L. INGRAM (member).—In 1891–95 I had the laying-out of about 500 miles of the boundary line between the United States and Mexico, from El Paso to the Pacific Ocean, and, although the country we passed through was bad enough, it was not as bad as the country we have seen on the screen to-night. From a technical point of view, I think the most interesting question with which we were concerned was, What is meant by a straight line on a spheroid? A straight line on a sphere is understood by surveyors to mean the arc of a great circle, but this definition is not applicable to a spheroid, which for practical purposes may be regarded as the shape of the earth. A line 500 miles long may vary in location as much as 10 feet at the center, according to the definition adopted for a straight line. The boundary which we were locating had two lines, one 260 miles long and one 150 miles long, which by treaty were required to be straight. I think we spent about three days in discussion and computation on this phase of the subject, and then found that as far as our lines were concerned the possible variation under any accepted definition of a straight line would be less than a single inch, which was much less than the probable errors of location.

There was one point brought out by Professors Tittmann and Doolittle, which is of considerable interest to geodesists, and that is the question of the variation of latitude. The reports that appear in the scientific journals from time to time are more or less indefinite and obscure. The general sense of these reports seems to be that the poles of the earth are not fixed, but perform what may be called a revolution around a mean point in an average period of about 425 days, with a radius varying from 0.16 seconds (16.3 feet) to 0.36 seconds (36.3 feet), the path of the moving poles being irregular and different on each successive revolution. The result of the constant shifting of the poles not only causes continual variation in the latitude of any given point, but all latitudes, longitudes, and azimuths become variable quantities, subject to an unceasing oscillation about their mean value. I would like to ask Professors Tittmann and Doolittle how far my statement of the case is correct, in the light of present knowledge, and what additional information may be available.

C. L. DOOLITTLE (visitor).-I was connected with the survey of the northern boundary, from the Lake of the Woods to the Rocky Mountains, from 1873 to 1874-75, when the work was done, and much of what Prof. Tittmann has been telling us is quite familiar to me as I have been over the ground myself. The work the Coast Survey is doing now is to restore the monuments of the boundary as we marked it.

I was much interested in the accuracy with which those monuments could be placed. In the determination of the parallel we made observations for latitude, which fixed a point on this parallel. We then ran the tangent, as we called it, to the next station, 20 miles or so distant. The offsets from the tangent

to the boundary adopted were the combination of the curvature of the parallel with the amount of station error, the latter due to local deviations of the plumb line. You never get a plumb line which will be an exact normal to the surface. There will always be a deviation; we never found a case where there was not considerable deviation. This question of variation of latitude, which Professor Tittmann has been talking about, and which I have been working on for the last twenty-five or thirty years, will give us a range from 50 to 60 feet, and on this account, if I determine the latitude today, and I determine it six or seven months from now with absolute precision, I would likely get a point of 40 or 50, or in extreme cases, 60 feet from the point I occupied before. Some one has said in regard to the 49th parallel that there is a strip of 50 or 60 feet wide that belongs alternately to one country and the other. In other words, the boundary varies 50 or 60 feet.

I think Professor Ingram's question can be readily answered, for I would say that we know very little about it. We know what is taking place, but as to the cause of it, and as for formulating a law for it, if we could predict what is going to happen ten years from now this might be possible, but we know very well we cannot. We thought some years ago that we were in line with the direct solution of this problem. The theory is very definite, and was worked out long ago by Prof. Euler, who established, theoretically, that there ought to be such a variation, and, assuming the earth to be a rigid body, he found a period of about 10 months; efforts were made for a long time to discover such a period or such a variation, but all of the attempts, as far as I know, were based on the supposition that the period was 10 months.

Well, different ones had more or less to do with it and I think I was a sort of pioneer in that direction myself. Instead of working at this theory I tried, by observation, to find out what was taking place. Professor Chandler, of Cambridge, who was more prominently connected with it in those days than anybody else, published with a good deal of confidence a conclusion that he had reached as a result of the analysis of many thousands of observations made at various places, that the variation had a period of about 14 months instead of 10 months, but that superimposed on that was another period of one year, and that the combination of the two produced the changes and irregularities that Professor Ingram referred to. This hypothesis can be made to fit the observations for a considerable period but it does not follow on to predict what is going to happen. You can take observations and fit such a curve to them but, if exterpolated a year or two ahead, it will not fit the observations at all. At present it is impossible to predict the position of the actual pole in regard to the mean pole. It appears to depend, to some extent at least, on meteorological causes, and if that really has much to do with it, it would be a proposition on the same order of difficulty as predicting the weather for long periods ahead. When we are able to solve this problem perhaps we may attack this latitude problem with some hope of success.