ing such a survey is to get a reliable determination of distance; but if some method is used that will give a determination of distance that will bear something like a constant ratio to the true distance I think you can, by correcting your work by frequent latitude observations, make a

survey of a considerable portion of country from which a good map can be constructed. The map that I made from about two months' work covered a piece of country about 300 miles long by 50 or 75 wide; the survey was made single-handed and I think was fairly

accurate.

Mr. Tyrrell: What method did you adopt in determining the variation ?

Mr. Stewart: The method I frequently adopted was, after observing for time, to take a number of compass bearings of the limb of the sun, noting the time, and then afterwards comparing the true bearing of the sun's limb from its declination at the time, its hour angle, and the known latitude.. Having found the true bearing in that way, a comparison of the compass-bearing gave the variation.

Mr. McDowall:-Suppose the country in one place was very level would it bear the same reduction of distance ?

Mr. Stewart:-It would not, strictly speaking; but in the long run errors would tend to compensate one another.

Mr. H. H. Gibson:-How closely can you determine latitude with a sextant ?

Mr. Stewart:-Comparing my different latitude determinations, I think with a marine sextant like mine, with an artificial horizon, you can get latitude within ten seconds, by making a number of determinations by circum-meridian altitudes, and taking the mean, assuming there is no eccentric error in your sextant. There might be a large eccentric error which should be determined.

President Ross:-You said you did the work single-handed. I suppose you had assistance to carry your outfit. I presume you speak of the instrumental work when you say that.

Mr. Stewart: Yes. Our party consisted of three besides myself, and then we had a couple of Indian guides and packers. I meant as far as the instrumental part of the work was concerned.

PAPERS.

[This Association is not responsible as a body for the opinions expressed in its Papers by Authors.]

LOCAL DEFLECTION OF THE PLUMB LINE.

BY OTTO J. KLOTZ.

In the present short paper it is only intended to lay before the Society certain data of the deflection of the plumb line as . found by latitude observations and azimuth surveys along the International Boundary, 49th parallel, from the Lake of the Woods to the Pacific Ocean. Those westward, as far as the Rocky Mountains, were published years ago in the United States Report of the Northern Boundary Survey, but those of British Columbia have, to my knowledge, never been published. The effect of deflection of the plumb line on longitude and azimuth observations is not considered in the present paper.

Deflection of the plumb line may be defined as the deviation of the vertical at any point from the normal at that point to the surface of an assumed figure of the earth. In dealing with the earth, we must assume its shape to be of some definite geometrical form and of certain dimensions, for only then can observations, at different points thereon, be correlated and adjusted. The best assumed form (Clarke's 1880 spheroid at present), however, differs at places widely from the actual form or geoid. To illustrate, if the continents were traversed by narrow canals, communicating with the ocean, their surface, although level, would be wavy or undulating, and would be in some places above, in other places below the surface of the spheroid or ellipsoid of revolution, the divergence of the two surfaces being probably confined to a few hundred feet.

The position assumed by the plumb line, is due to the law of gravitation, that is, it is the integrated result of the attraction of the individual particles, composing the mass of the earth, and hence the position is affected by the relative distribution of them. We may, therefore, say that the unsymmetrical distribution of the particles, whether on the surface, as mountains, etc., or in

the thin crust, is the cause of the deflection of the plumb line from its theoretical position. The ablest mathematicians have been engaged, ever since the era of precise measurement, upon this difficult question of the form and dimensions of the sea level surface.

In some instances we are quite prepared to find local deflections of the plumb line, for example, when observations are taken on the plains at a point near a more or less isolated upheaval, as the Three Buttes or Sweet Grass Hills in Montana, just south of the International Boundary. These hills, as we shall see later, pulled the 49th parallel out of its theoretical position about 800 feet. On the other hand, large deflections show themselves without any visible reason or cause as evolves from numerous observations and their geodetic connection. A remarkable instance is that of the comparatively plain area surrounding Moscow, which I visited recently, where, on the margins of an eighteen mile east and west zone, large deflections of opposite signs were found. From this it must be concluded that there exists beneath the surface a cavity or at least matter of small density.

It is evident, therefore, that the observations alone, at any particular point, are not conclusive for fixing its geographical position upon the surface of the earth, but that numerous astronomically determined points must be connected linearly by triangulation, and from their inter-accordance, or discordance, the most probable values determined, based upon an assumed figure of the earth.

In our own city here (Ottawa), there appears, due to the topographical configuration, to be a deflection of the plumb line; for, the latitude determinations made by me at the observatory on the summit of the escarpment, compared with those made some years ago by Mr. Lindsay Russell on the opposite side of the river, show a discrepancy of about a second of arc, equal to about a hundred feet, a quantity greater than the error of observation. However, a more or less extended hypsometric survey would be necessary for a plausible a priori conclusion with reference to the probable discordance in latitude to be expected between two stations.

All observations for the determinations of positions upon the earth depend upon the direction of the vertical. Latitude and longitude observations, the surveyors' and engineers' operations, all have their zero of reckoning in the centre of the level bubble,

and any displacement of the latter, which is equivalent to the displacement of the plumb line, affects the results, and will show discordances when widely separated observations are geodetically connected.

It may be stated that a delicate level used for latitude work, reading to a second of arc, has usually a radius of about 1,700 feet, or nearly a third of a mile, for the curve ground on its inner upper surface.

To digress for a moment.

Boundary lines may be divided into three classes: those representing a social unity, those representing a physical unity, and those representing a political unity. Those of the first find the largest number of representatives in the older settled countries, for the primal concept of boundary was to conserve the social unity. It was not to define territorial extent as much as to define or assert the domain of a like people; like by language, race, or religion or other affiliation. Such boundaries are, as a rule, very irregular and difficult to describe. When the social organism reached that development that written treaties became necessary between adjoining peoples, the description of the separating boundary was made from the boundary de facto, and the boundary not laid down from the description.

The second class we may consider an expansion of the first, resulting from conquest, whereby a physical as well as a social unity was to be preserved. Of the physical boundaries— mountains, rivers and lakes-to serve the purpose of barriers, by mountains, that end is undoubtedly best attained. Europe furnishes a number of examples of this.

The third class, which we may call the astronomic boundary, is a development of recent times, and applies invariably to areas practically unsettled, unsurveyed and little known. Such can be laid down on paper, or described in treaties without scarcely any knowledge of the country whatsoever.

While Europe furnishes the most examples of the first, America does so of the last. Many of the State boundaries of the United States are astronomic lines, either meridians, parallels, or lines of definite azimuth. Similarly with the subdivision of Australia and recent boundaries in Africa. Astronomic boundaries may generally be taken as an index of the ignorance existing of the country or area involved and its resources.

Boundaries under the first division are difficult for definition or restoration when such is necessary. Those of the second,