398 



SCIENCE. 



[N. S. Vol. II. No. 39. 



1. Development of Some Useful Quaternion Expressions, 

 with Applications to Geometry of Three and Four Di- 

 mensions : James Byknie Shaw. 



2. The Constant of Aberration : C. L. DOOLITTLE. 



3. On the Constant of Adulation : S. C. Chandler. 



4. Progress of the Zone Work at the Naval Observa- 

 tory, Washington : A. N. Skinner. 



5. On the Distribution and the Seculan Variation of 

 Terrestrial Magnetism (read by title) : L. A. Bauer. 



6. Sun Spots and Blagnetic Storms : M. A. Veedee. 



7. The Spectrum of B. Lyrx: Edwin B. Frost. 



8. Notes on Square Numbers Whose Sum Is Either a 

 Square or the Sum of Other Squares : Artemas 

 Martin. 



9. Some Hesults for Stellar Parallax from Meridian 

 Transit Observations at the Washburn Observatory: 

 Albert S. Flint. 



10. A Convenient Formula for Computing Times of Moon 

 Bising : EDGAR Frisby. 



11. On a Slide Scale for Computing Precession: Edgar 

 Feisby. 



12. Chronology and Ancient Eclipses : Samuel W. 

 Balch. 



13. Period of B. Comse : Henry Parkhurst. 



In his paper Professor Shaw develops the 

 alternating functions, A.pq = ^ (pq — qp, 

 S. p Aqr 



A. pqr = S. p Aqr — ■ Sp. A. qr, 

 — Sq. Arp — Sr. Apr, 

 S. p Aqrs. 



A set of four quaternions related to one 

 another is deduced, analogous to a set of 

 three rectangular unit vectors and from 

 which various collections of formulas can 

 be derived. 



Affixing one of the set of four quaternions 

 to each vertex of a tetrahedron and letting 

 the point P = Xj Ij + x„ Ij + Xg I3 + x^ I4 

 be that point for which the volumes 

 EC, P— BCD, P — CDA,"P — DAB, P— 

 ABC are as x, : Xj : X3 : x^ we are enabled 

 to treat solid geometry projectively. 



The elaborate and carefully arranged 

 series of observations made by Professor C. 

 L. Doolittle at Lehigh University, primarilj^ 

 for the determination of the variation of 

 latitude, was planned by him so that a de- 

 termination of the constant of aberration 

 could also be secured, stars being taken 



throughout all the 24 hours, and the pairs 

 being observed before and after midnight 

 so as to obtain maximum aberration co- 

 efficients, with opposite sign. This series 

 was observe'd from 1892, October 10, to 

 1893, December 27, 442 nights. 



Professor Doolittle finds for the constant 

 of aberration 



20."55, 



Struve's value being 20. "44. Later values 

 differ considerably from that of Struve, and 

 it would appear that his value is too small. 

 Dr. Chandler, on examining Pond's 

 Greenwich mural circle observations with 

 the idea of getting at the long period term 

 of the variation of latitude, found the work 

 to be of excellent quality, quite as good as 

 the modern work, though imperfectly re- 

 duced. The plan of observation was first- 

 rate, being so arranged as to eliminate as 

 far as possible division errors, flexure and 

 all instrumental constants. Indeed, Dr. 

 Chandler regards the discovery of the good 

 quality of this work as a most important 

 one. From Pond's observations is found 

 for the constant of lunar nutation 



9."190, 

 the usual value, called Peters', being 



9."223. 

 Peters observed only a few stars and took 

 no account of the long period variation of 

 latitude. It is probable that the constant 

 of lunar nutation is very nearly 



9."20, 

 since Professor Newcomb finds for this con- 

 stant from the Greenwich "transit circle dec- 

 linations and the Washington transit circle 

 declinations respectively 



9."194, 



9."204. 

 It should be noted that Dr. Chandler's 

 discussion of Pond's mural circle declina- 

 tions confirms Boss' proper motions as being 

 almost exact. 



