132 



SCIENCE. 



[N. S. Vol. XVI. No. 395. 



the choice of base. The volume of a poly- 

 hedron is defined as the sum of the volumes 

 of a set of tetrahedra into which it is cut, 

 this sum being proved independent of the 

 mode of partition into tetrahedra. Then 

 a prismatoid is defined, and its volume 

 proved 



r=^{B + 3S). 



Then all the ordinary solids are forms of 

 prismatoids. 



A New Solar Attachment: Herbert A. 

 Howe, Director of the Chamberlin Ob- 

 servatory, University Park, Colorado. 

 This was a description of a small solar of 

 simple construction devised by Mr. Orville 

 F. Shattuck, a former pupil of Professor 

 Howe. It was shown how the device, when 

 attached to a universal instrument or engi- 

 neer 's transit, may be used for some simple 

 astronomical observations, and for illustra- 

 ting the principles of the equatorial coude, 

 the prism transit, the sextant and the almu- 

 cantar. 



On the Periodic Solutions of the Problem 

 of Three Bodies: Professor E. 0. Lovett, 

 Princeton University. 

 Lagrange found five exact solutions of 

 the problem of those bodies in each of 

 which the bodies preserve an unvarying 

 configuration which revolves with a uni- 

 form velocity. When the third body is of 

 infinitesimal mass compared with the other 

 two, it can describe small periodic orbits in 

 the vicinity of the points where exact solu- 

 tions exist. The latter points were called 

 centers of libration by Gylden, and Darwin 

 calls the infinitely small body an oscillating 

 satellite. Hill pointed out the fertility of 

 the notion and made a splendid application 

 of it in his lunar theory. Poincare elabo- 

 rated the mathematical theory in his cele- 

 brated researches and we owe to Darwin an 



extended collection of examples of periodic 

 orbits. 



One of the most recent investigations of 

 such orbits is a suggestive paper by 

 Charlier, in No. 18 of the Meddelanden 

 frun Lunds Astronomiska Observatorium. 

 In the Monthly Notices of the Royal Asti'o- 

 nomical Society for November, 1901, 

 Plummer has discussed some of Charlier 's 

 results in a more general manner. 



It is the object of Professor Lovett 's 

 paper to determine the imaginary centers of 

 libration and their corresponding orbits, 

 and thus complete the analytical solution 

 proposed by Charlier. The results cannot 

 be expected to fit the sky, but they may be 

 of some interest to mathematical astron- 

 omers. It appears that there are real 

 periodic orbits corresponding to imaginary 

 centers of libration. 



Til e Bate of the Biefier Sidereal Clock, No. 



56: Professor Charles S. Howe, Case 



School of Applied Sciences. 



In this paper Professor Howe gave the 

 details and results of some careful series of 

 experiments of a Riefler clock enclosed in a 

 glass case from which the air had been par- 

 tially exhausted. The mean daily rate for 

 a trifle over three months was .116 of a 

 second. The average daily variation from 

 this mean was .015, and the maximmn vari- 

 ation .022 of a second. The paper will be 

 published in the Astronomische Nach- 

 richten. 



A Bepresentation of the Coordinates of the 

 Moon in Power Series which are Proved 

 to Converge for a Finite Interval of 

 Time: Dr. P. R. Moulton, University of 

 Chicago. 



It is proved in this paper that the differ- 

 ential equations which the motion of the 

 moon must fulfill can be integrated as 

 power series in certain parameters, and that 

 the series converge for at least a certain 



