608 



SCIENCE 



[N. S. Vol. XXV. No. 642 



function is determined to suit the bound- 

 ary conditions, by the image-method; and 

 it is shown that one of the stream lines 

 breaks up into the median line of the 

 channel and a symmetrical oval. The 

 strength of the doublet can be so adjusted 

 that this oval does not differ appreciably 

 from a given circle when the latter does not 

 occupy more than half the breadth of the 

 channel. 



Preliminary Wave-lengths af Flash Spectra 



taken in Spain, Aii,gust 30, 1905: Dr. S. 



A. Mitchell, Columbia Univei*sity, New 



York City. 



The wave-lengths were obtained from 

 photographs taken by the writer -while a 

 member of the United States Eclipse Ex- 

 pedition. The spectrograph was a four-inch 

 grating of 14,438 lines per inch ruled on a 

 parabolic surface, which was used without 

 slit. Weather conditions were splendid. 

 The photographs are remarkable for their 

 splendid detail throughout their whole 

 length from D^ to 3,300. There are about 

 five thousand measurable lines in this re- 

 gion. The dispersion of the grating is 

 about the same as for the ' Bruce three ' 

 spectrograph of the Yerkes Observatory 

 and the Mills spectrograph of the Lick Ob- 

 servatory, the distance from D^ to H being 

 seven inches. 



On the Minimum Number of Operators 

 whose Orders exceed Two in any Finite 

 Group: Dr. G. A. Millee, University of 

 Illinois, Urbana, 111. 



When just half of the operators of a 

 group are of order 2 the order of the group 

 is twice an odd number, and all the opera- 

 tors of odd order together with the identity 

 constitute an abelian subgroup whose order 

 is half the order of the group. Professor 

 Miller's paper has for its main object the 

 proof of the following theorems: If the 

 order (g) of a group is written in the form 



Pi; P2! ■ ■ ; pk being distinct odd prime 

 numbers and a^ > 0, the number of the 

 operators whose orders exceed 2 can not be 

 less than 



Moreover, it is possible to construct a 

 group in which the number of operators 

 whose orders exceed 2 is exactly equal to 

 this number. If a group of order g con- 

 tains the smallest possible number of oper- 

 ators whose orders exceed 2, the sub-group 

 which is composed of all its operators 

 which are commutative with one of the 

 non-invariant operators of order 2 con- 

 tains no operator whose order exceeds 2. 

 This sub-group is a Sylow sub-group and 

 just half of the remaining operators are of 

 order 2. 



Results of Physical Observations on the 

 Saturnian System ivith the 18-inch Clark 

 Refractor: Professor David Todd, Am- 

 / herst College, Amherst, Mass. (Pre- 

 sented by title.) 



With the exception of those papers which 

 appear upon the joint program of Fri- 

 day morning, as given above, the papers of 

 Section A were presented in connection 

 with the program either of the Mathe- 

 matical or of the Astronomical Society, 

 according to the subject matter treated in 

 each case. This arrangement was made in 

 accordance with a resolution adopted at the 

 Ithaca meeting to the effect that ' the sec- 

 tional committee be empowered to turn over 

 technical papers to the technical societies.' 

 Laenas Gippord Weld, 



Secretary 



THE ASTRONOMICAL AND ASTR0PHY8IGAL 

 SOCIETY OF AMERICA 



II 



A New Form of Meridian Mark: G. W. 



Hough. 



Two years ago I established a meridian 

 mark in order to study the change of azi- 



