NOVEMBER 19, 1897.] 
physical research in our own generation 
were stricken out! 
The future should look bright, indeed, as 
we view it to-day. Munificence and skill 
have provided this splendid observatory 
with means for promoting knowledge in both 
the older and the newer branches of the 
sublime science to which it is dedicated. 
Its magnificent equipment will be used by 
men who have won merited distinction in 
both the older and the newer methods of re- 
search. It has the cooperation and support 
of a great institution of learning. From 
this happy union of ability and opportunity 
we have reason to expect results of the 
highest import to the new astromony, and 
to its allied branches of physical science. 
But, lest any words of mine should give 
rise to expectations that may not be fulfilled, 
I wish to say once more that important re- 
sults are not necessarily of a striking or sur- 
prising character. We can hardly assume 
that every increase in telescopic power will 
be followed by the discovery of new planets 
or satellites. Such discoveries, if they come, 
will be welcome ; but they should not be ex- 
pected. There may be no more planets or 
satellites, yet undiscovered, in the solar sys- 
tem. But we may confidently expect from 
the work of this observatory those results 
which throw light on the dark places in na- 
ture, and which, therefore, though they may 
not stimulate the popular imagination, are 
of the very highest importance, for they are 
indispensable to true scientific progress. 
James H. Keener. 
ALLEGHENY OBSERVATORY. 
MATHEMATICS AND ASTRONOMY AT THE 
AMERICAN ASSOCIATION FOR THE AD- 
VANCEMENT OF SCIENCE. 
Tue officers of the Section of Mathe- 
matics and Astronomy were as follows: 
Chairman, W. W. Beman; Secretary, J. 
McMahon; Press Secretary, P. A. Lambert; 
Councillor, E. W. Hyde; Sectional Commit- 
SCLENCE. 
755 
tee, W. W. Beman, J. McMahon, A. Mac- 
farlane, W. F. Durand, J. E. Kershner, 
W. 5S. Pritchett; Member of Nominating 
Committee, A. Ziwet; Committee to nom- 
inate officers of Section, W. W. Beman, J. 
McMahon, A. Hall, Jr., R. S. Woodward, 
A. Macfarlane. 
The Chairman’s address was on ‘A Chap- 
ter in the History of Mathematics,’ which 
has already been published in this JourNAL. 
The following papers were presented to 
the Section : 
1. A Problem in Substitution-groups. 
By Dr. G. A. Miller, Rosette, Kan. 
2. Continuous Groups of Spherical Trans- 
formations in Space. By Professor H. B. 
Newson, Lawrence, Kan. 
3. The Treatment of Differential Equa- 
tions by Approximate Methods. By Pro- 
fessor W. F. Durand, Ithaca, N. Y. 
4. Commutative Matrices. By Professor 
J. B. Shaw, Jacksonville, Tl. 
5. On the Theory of the Quadratic Equa- 
tion. By Professor A. Macfarlane, Lehigh 
University, South Bethlehem, Pa. 
6. A New Principle in Solving Certain 
Linear Differential Equations that occur 
in Mathematical Physics. By Professor A. 
Macfarlane, Lehigh University, South Beth- 
lehem, Pa. 
7. Condition that the Line Common to 
nm—1 Planes in an n-space may Pierce a 
Given Quadric Surface in the Same Space. 
By Dr. Virgil Snyder, Ithaca, N. Y. 
8. The Psychology of the Personal Equa- 
tion. By Professor T. H. Safford, Williams- 
town, Mass. 
9. Compound Determinants. (Prelim- 
inary communication.) By Professor W. 
H. Metzler, Syracuse, N. Y. 
10. Waters within the Earth and Laws of 
Rainflow. By W. 8S. Auchincloss, C.E., 
Philadelphia, Pa. 
11. On the Secular Motion of the Earth’s 
Magnetic Axis. By Dr. L. A. Bauer, Uni- 
versity of Cincinnati, Cincinnati, O. 
