February 3, 1905.] 



SCIENCE. 



177 



Tilt Computation of tJtc Deflections of the 

 Vertical due to the Topography Sur- 

 rounding the Station: Professor J. F. 

 Hayford, Coast and Geodetic Survey, 

 Washington, D. C. 



The computation of deflections of the 

 vertical depending upon the topography 

 surrounding a station is of fundamental 

 importance in connection with new investi- 

 gations of the figure of the earth. Such 

 computations have been available in but 

 few cases because of the difficulty of mak- 

 ing them. The method now in use by the 

 Coast and Geodetic Survey was fully 

 shown. Such computations by this method 

 have already been made at 250 astronomical 

 stations in the United States, in each of 

 which account is taken of the topography 

 wdthin a circle surrounding the station 

 having a radius of more than 2,500 miles. 



Extension of a Theorem due to Sylow: 

 Professor G. A. Miller, Stanford Uni- 

 versity, Cal. 



Every group G of order p"', p being any 

 prime number, contains at least p invariant 

 operators. This fundamental theorem, 

 due to Sylow, is included in the following: 



Every non-abelian group of order 

 contains at least jj invariant commutator 

 operators, and its commutator quotient 

 group is always non-cyclic. The paper is 

 devoted to a proof of this theorem and the 

 following closely related theorems: 



It is possible to construct a non-abelian 

 group having any arbitrary abelian group 

 as a commutator quotient group. 



Every non-cyclic abelian group of order 

 p« is the commutator quotient group of 

 some non-abelian group of order p"'. 



On Inversions: Professor J. J. Quinn, 

 Warren, Pa. 



Mr. Qi;inn exhibited and explained a 

 number of new linkages for describing the 

 right line, in each of which the principle 

 of inversion was applied. 



On Systematic Errors in Determining 

 yariatio)is of Latitude: Mr. Prank 

 ScHLESiNGER, Ycrkes Observatory, Wil- 

 liams Bay, Wis. 



Observations for the variation of lati- 

 tude seem to be subject to certain sys- 

 tematic errors. In this paper two con- 

 temporaneous series made near Honolulu 

 in 1891 and 1892 are discussed and com- 

 pared. The method of separating the sys- 

 tematic errors common to both series from 

 the accidental is indicated, the conclusion 

 being that there is present some source of 

 error common to both observers and there- 

 fore probably beyond their control. This 

 result is shown to be independent of any 

 assumption regarding the variation of lati- 

 tude diiring the period under discussion. 



Some Experiments on the Distortion of 

 Photographic Films: Mr. Frank Schles- 

 INGER, Yerkes Observatory, Williams 

 Bay, Wis. Read by title. 



Bibliography and Classification of Mathe- 

 matical and Astronomical Literature at 

 the Library of Congress: Mr. J. D. 

 Thompson, Library of Congress, Wash- 

 ington, D. C. 



Attention was called to the printed cards 

 issued by the Library of Congress for 

 books and pamphlets on mathematics and 

 astronomy in its collection and it was ex- 

 plained how these may be used to great 

 advantage in the special libraries of the 

 mathematical departments of universities 

 and of observatories. The classification 

 scheme used at the Library of Congress was 

 also explained. This paper will be printed 

 by the Library of Congress. 



On an Optical Method of Radial Adjust- 

 ment of the Axes of the Trucks of a 

 Large Observatory Dome: Professor 

 David Todd, Director Amherst College 

 Observatory, Amherst, IMass. 

 The larger dome of the new observatory 



of Amherst College is mounted on fourteen 



