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REPORT OF SPECIAL AGENT OF TRANSPORTATION FOR THE ASSOCIA

TION TO ACT WITH THE LOCAL COMMITTEES.

In regard to the efforts to secure reduced fares for members attending the meeting: The membership of the A. A. A. S. being distributed over so large an extent of country several distinct Passenger Agents' Associations are included therein, each of which require separate negotiations in obtaining concessions. The rules and regulations of the associations are unlike, therefore unity and uniformity of action cannot be obtained of all, especially from those most distant from the place of meeting.

The rules of the principal associations are now such that the chairman of the association can, under definite limitations, grant concessions for fares without submitting the question to a vote of the passenger agents of the association.

The A. A. A. S. can feel reasonably certain of obtaining a concession in the Passenger Association where the meeting is held, also in the adjacent associations, of a fare and one-third for the round trip, on the certificate plan and three days' limit.

The requirements of such a concession are that one hundred members attend the meeting from two of the associations. This does not meet all cases, but is the best which can be obtained without a special vote by the different Passenger Agents' Associations, which is no easy matter to obtain.

For the Cleveland meeting I applied to the principal associations for a concession of our fare for the round trip and an extension of the three days' limit. Neither was granted.

Before the associations will take any official action for a reduction of rates, an application must be filed stating the name of the organization, place of meeting, date of meeting, the probable number in attendance and the name of the secretary who will sign the certificates.

All of this information can be furnished by the agent except the name of the secretary who is to sign the certificates.

The name of the latter should be designated by the Local Committee for the next meeting by the first of January, 1889.

The date of the meeting should be counted from the time the council meets and adjourns.

P. H. DUDLEY, Honorary Agent.

SECTION A.

MATHEMATICS AND ASTRONOMY.

OFFICERS OF SECTION A.

Vice President.

ORMOND STONE of University of Virginia, Va.

Secretary.

C. L. DOOLITTLE of Bethlehem, Pa.

Member of Council.

WILLIAM HARKNESS of Washington.

Members of Sectional Committee.

H. A. NEWTON of New Haven, Conn., HENRY M. PAUL of Washington, R. S. WOODWARD of Washington.

Member of Nominating Committee.

E. W. HYDE of Cincinnati, Ohio.

Members of Sub-committee on Nominations.

G. C. COMSTOCK of Madison, Wis., ALVAN G. CLARK of Cambridge, Mass., C. H. ROCKWELL of Tarrytown, N. Y.

ADDRESS

BY

PROFESSOR ORMOND STONE,

VICE PRESIDENT, SECTION A.

MOTIONS OF THE SOLAR SYSTEM.

As in the moral world unselfishness stands high above all other virtues, so in science the interest in any subject depends principally upon its relation to other subjects. Thus pure mathematics derives its chief value from its applications or from the possibility of application. Astronomy affords the highest opportunities for the exercise of genius in the development of geometrical analysis. But its real interest does not centre in the analysis itself, but in its application to the study of the motions of the physical universe; nor is it the motions themselves which excite our chief interest, but rather those philosophical questions which relate to the origin, structure and unity of the universe.

No other hypothesis has been suggested which offers such direct and complete answers to most of these questions as Newton's law of gravity. It is but natural, therefore, that the majority of the problems which arise in regard to the motions of the solar system should have their origin in an effort to confirm this law, so remarkable for its wonderful simplicity, yet so complicated in its consequences, that many of the most important problems arising therefrom remain still unsolved.

The first attempt to apply Newton's law to all the motions of the solar system was made by Laplace, and to-day there exists no work in science which for boldness of design, grandeur of outline,

and success of accomplishment, surpasses the Mécanique Céleste. Nevertheless, when Lindenau and Bouvard undertook to compute their tables of the motions of the planets, a complete revision of Laplace's theory was found necessary. This was due to the fact that Lindenau and Bouvard had more numerous and more accurate observations with which to compare Laplace's theory than the latter had employed in its formation. Every advance in accuracy of observation demands a corresponding advance in theory.

As no general solution of the problem of more than two bodies has thus far been obtained in finite terms, in any analytical discussion of the motions of any dynamic system, it is necessary to resort to the use of infinite converging series. Now, it is a peculiarity of such series, that the expressions involving small quantities of any given order of magnitude are generally more complicated than those of a lower order, although in general the former are much smaller than the latter. Mr. Hill, in speaking of his computation of the inequalities of Jupiter and Saturn, especially mentions that more time was consumed in computing terms of three dimensions than in computing those of two. On the other hand, every additional observation adds to the work of the computer. Such are some of the difficulties which beset the computer in his efforts to obtain numerical solutions of problems in celestial mechanics.

So enormous, indeed, is the labor involved, that there exists besides those mentioned only one other complete set of theories and tables of the motions of the principal planets, that of Leverrier. Leverrier's tables of the inner planets are now nearly thirty years old, and those in use to-day, if we except Hill's tables of Venus, which were published in 1872, in which Leverrier's theory was employed, but corrected by comparison with observations. Leverrier's tables of the outer planets are much later, having engaged his attention almost to the day of his death. His tables of Jupiter and Saturn were published in 1876 and those of Uranus and Neptune during the following year. Bouvard's tables of Jupiter and Saturn preceded those of Leverrier no less than fifty-five years.

Newcomb's tables of Neptune were published in 1865, those of Uranus in 1874. Hill's Theory of Jupiter and Saturn which has for years occupied his attention has at last been completed, and he is now engaged in preparing tables therefrom. These are intended to form a part of a complete series of tables of the principal planets now being prepared under the direction of Professor New

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