PROCEEDINGS. 
371 
Mr. F. G. Radelfinger reported on Progress in pnre mathe¬ 
matics in 1900. In publications, the new Mathematical Ency¬ 
clopedia and Forsyth’s Differential Equations are specially note¬ 
worthy. A brief historical sketch of the treatment of differential 
equations from the time of Briot and Bouquet introduced an 
outline of Painleve’s recent and successful attack on the equa¬ 
tions of the second order. [Published in this volume, p. 157.] 
Mr. T. J. J. See reported on Progress in astronomy in 1900. 
The principal matters were the publication of the results of the 
observations on the transit of Venus; the observations on Eros; 
the discovery of several hundred new double stars, and the pub¬ 
lication of double star catalogues ; and the observations at the 
Naval Observatory on the diameters of the planets with a color 
screen. [Published in this volume, p. 145.] 
Mr. Hussey, of the Lick Observatory, made some brief re¬ 
marks. 
5S2d Meeting. March 16, 1901. 
President Walcott in the chair. 
Thirty persons present. 
Mr. M. Updegraff read a paper on the Errors due to imper¬ 
fections in the pivots of a theodolite. By a mathematical analy¬ 
sis he finds that with the modern bearings consisting of two con¬ 
vex cylindrical surfaces on which the pivot rests, any ellipticity 
of the pivot gives rise only to errors in azimuth when the pivot 
is rotated. [Published in Astronomische Nachrichten, No. 3712, 
May, 1901.] 
A general discussion followed, participated in by Messrs. 
Green, Hayford, Bigelow, Paul, Wead, E. G. Fischer, Eim- 
beck, and Littlehales. Mr. Fischer pointed out that the 
eccentricity which could be discussed mathematically was far 
less in magnitude on the best modern pivots than the errors aris¬ 
ing from inequalities in the steel, and from the unequal wear 
which is found even after a short use. 
Mr. W. J. Hussey, of the Lick Observatory, gave, by invita¬ 
tion, An informal account of recent work at that Observatory. 
50—Bull. Phil. Soe., Wash., Vol. 14. 
