uncertainty of the measured lengths of the arcs is extremely small, compared with that of their amplitudes or differences of latitude; since the latitudes are affected by the irregularities of local attraction to an amount generally between one and two seconds of an arc, attaining in mountainous regions even ten seconds. Stations exhibiting extraordinary discrepancies in latitude are, of course, excluded from the discussion, which was preceded by a minute comparison of all the standards of length that had served in the several operations. The following arcs, entitled to equal consideration by their superior precision, have entered into the comparison: 1. The French arc, from Formentera (lat. 38° 40') to Dunkirk (lat. 51° 02'), having an amplitude of 12° 22', and comprising six latitude-stations. 2. The British arc, from Greenwich (lat. 51° 28') to Saxavord (lat. 60° 49′), amplitude 9° 21', with six latitude-stations. 3. The Indian arc, between Punnae (lat. 8° 10) and Koliana (lat. 29° 31′), amplitude 21° 21', with eight latitude-stations. 4. The Russian arc, from Staro Nekrassowka (lat. 45° 20') to Fuglenoess (lat. 70° 40'), amplitude 25° 20'; thirteen latitude-stations. 5. The Cape of Good Hope arc, from North End (lat. 29° 44') to Cape Point (lat. 34° 21'), amplitude 4° 37'; five latitude-stations. 6. The Peruvian arc, from N. lat. 0° 02' to S. lat. 3° 4', amplitude 3° 06'; two latitude-stations. These six groups, aggregating an arc of over 78°, and comprising forty latitude-stations, when treated with reference to a spheroid of revolution, yield the following results:

When the latitudes of the several stations are computed from the mean of each arc upon these elements, the difference between the computed and observed latitudes is on the average 1"-8, a degree of discordance fairly ascribable to local deviations of the plumb-line. A quadrant of the meridian of the above spheroid is equal to 10,001,887 metres, showing that the metre falls short of its presumed value by its 1-5300th part, equivalent to about

one foot in a mile.

The same data, treated with reference to an ellipsoid of three axes, indicate an ellipticity of the equator of 1:3270, while the

average error of the latitudes is reduced to 14. This better representation of the observations by the assumed figure corresponds, however, only to the introduction of three, instead of two, unknown quantities into the problem, and furnishes no evidence that there is really a general ellipticity of the equator. Such a conclusion could only be reached by the evidence of many more arcs measured near the equator, in different longitudes, than we now possess.

Since the U. S. Coast Survey arcs, from Mt. Blue in Maine to Nantucket (1868), and from the head of Chesapeake Bay to Ocracoke, N. C. (1875), comprising 8° and swelling the aggregate to 84° of latitude, accord closely with the elements of Clarke's spheroid (1866), it appears that this figure may be taken as the most probable that can be deduced from geodesic measurements published at the present time; nor is it likely that they will be ma-terially changed by the operations now in progress in Central Europe. It is only when larger arcs shall have been measured in North and South America, in Siberia, Africa and Australia, that we may look for a more accurate knowledge of the figure of our globe.

Such exact determination of the earth's form and magnitude has an interest quite apart from the problem of perfectly mapping its surface. Its equatorial diameter is the unit of measure for all distances in our planetary system, by means of which we are enabled to compare them with distances appreciable to our perception. By ascertaining the fact that its actual figure is that of equilibrium of a fluid body rotating at the same rate, we establish a degree of probability, almost amounting to demonstration, that it once was in a fluid state, and thus obtain a sound link in the chain of evidence for our received conception of the probable history of our solar system. But it is mainly in looking forward to the probable continued existence of mankind through time comparable in duration with what is called geological time, that we find a just incentive to extreme accuracy in our geodesic work. If in that remote future it should be possible to determine, by a repetition of our operations, what changes the dimensions of the earth have undergone during the intervening time, how appreciative will be the man of that day of the endeavors of our age, which he will look upon as lying at the very beginning of exact knowledge.

The permanence of the earth's magnitude involves not only our measure of space, but also that of time, since the revolution of the earth about its axis is our only available unit, and a contraction of its dimensions would inevitably cause an increased rate of rotation.

We cannot presume that our several individual achievements, however marked in our day, will remain distinguishable after a million of years in the report of the aggregate advance of the chiliad in which we have lived. Eminence in political history and in literature is surely doomed to oblivion, because the interests involved in the one, and the modes of thought and habits of life portrayed in the other are transient. If any names are destined to go down to such remote posterity it must be those of the fortunate ones who have been enabled to announce to mankind the discovery of great laws of nature, that endure forever. Among the most permanent monuments of science is the work of Geodesy. The interests of an intelligent race of inhabitants of our globe in its cosmic history can never fail. Well ascertained facts relative to the size and form of the earth, from the remotest epochs, will ever retain their importance. I desire to proclaim as loudly as I can, that there is no monument so enduring that could be erected for himself by one of our great money-princes, as the establishment of a Geodesic fund for the measurement of extensive arcs of meridians and parallels. Deservedly called by the name of the Founder, his fame would go down to the remotest generations of man.

Now, before taking leave of you, I will permit myself to say a few words, to enforce what I have sought to imply in my introductory remarks, on the part which abstract thought and pure mathematics have had, and necessarily must have, in the development of human knowledge. In doing this I desire particularly to recall Prof. Newton's plea for a more extended study of "the science that draws necessary conclusions," as Peirce has defined it. It is the science that develops the absolute modes of thought, and all other sciences must be subject to it, whenever they become sufficiently advanced to undertake to account for cause and effect in measure as well as in mode. In physical science, in chemistry, the work that now remains to be done in order that we may understand the constitution of the material elements, and predict the result of experiments, is almost purely mathematical. Here lies

the golden key that will unlock the mystery of the microcosm. It is not given to every one to pursue with success the study of abstract science—non omnibus licet adire Corinthum:- but let every student who loves mathematics and to whom the simpler forms of mathematical thought have come as by intuition, without effort and with a sense of great delight-this is the test of the gift- let him believe that there is a great prize within his reach and devote himself to pure science.

How much remains to be done! If we are to interpret the qualities of molecules, as arising from the combined effect of numberless atoms moving in orbits constrained by mutual influences-how must we despair of any exact interpretation of the microcosm when we reflect that we have not yet sufficiently developed our modes of thought to enable us to take into account in the macrocosm of the heavens the mutual interaction of more than two bodies, except by processes of approximation unsatisfactory to the mind and impossible when extended to many bodies. But shall we allow ourselves to be discouraged and say: nay, this is too troublesome, let it go; matter is very well as it is and it is useless to inquire how it came to be so; we will eat and drink and be merry, for to-morrow we die? Never! We want to know !! The Promethean fire is deathless; to seek to know the causes of things rerum cognoscere causas-is a Divine quality of our nature that we cannot divest ourselves of, fraught though it be with unrequited labor and pains. WE WANT TO KNOW! and as our revered President told us at the opening of the session, with the retrospect upon a long life, in which wisdom has been the fruit of much seeking to know, there is no satiety of knowledge. Friends, to my mind this insatiate desire to know the causes of things, and to understand the ways of creation, is the strongest evidence that there is a Divine mind from which the human mind is derived, and that man has been made in the image of God.

REPORT OF THE COMMITTEE ON WEIGHTS,

MEASURES AND COINAGE.

IN conformity with the design of its institution, which was to bring to the notice of the Association, from time to time, such subjects as seem to call for their action or the expression of their opinions, the Committee on Weights, Measures and Coinage beg leave first, to submit a statement of the progress made in the effort to secure the participation of the government of the United States in the establishment of an International Bureau of Weights and Measures; and secondly, to invite attention to certain questions of grave importance now agitating the public mind, concerning the principles which should govern legislation in regard to standards of value, in the decision of which, in the view of the Committee, are largely and directly involved the material interests and welfare of the people of the United States, and indirectly those of the whole civilized world.

First, as to the International Bureau of Weights and Measures. In the report of this Committee presented to the Association at the annual meeting of 1875, held at Detroit, the fact of the then recent negotiation of an international convention, to which the Government of the United States had been an assenting party, for the establishment and permanent maintenance of an institution for the preparation and verification of standards of measurement, and the preservation unaltered forever of the prototypes from which such standards are derived, was stated, accompanied by a resolution that a memorial to Congress be prepared for signature by members. of the Association and others, praying the Senate to ratify the action of the Executive Department in entering into the Convention, and praying Congress to make provision to discharge the obligations resting upon us in consequence of our adhesion to such convention, which resolution was unanimously adopted.

In compliance with the requisitions of this resolution, the proposed memorial to Congress was prepared without delay, and was