120 SCIENCE PROGRESS 



system of referring a paper to expert referees ensures this in 

 most cases. 



Dr. D. M. Y. Sommerville {Proc. Edinb. Math. Soc, vol. xxxii. 

 1914) discusses an error in one of Gauss's three proofs of the 

 reciprocity of parallelism. This seems to indicate matters of 

 historical interest as regards the order in which Gauss devised 

 these proofs ; and it is of some interest that neither Bonola nor 

 his German translator noticed Gauss's fallacy, but Carslaw, the 

 English translator of Bonola, did. In 1914 Dr. Sommerville 

 published an excellent text-book on The Elements of Non- 

 Euclidean Geometry (London : G. Bell & Sons, Ltd., 5s.). Also 

 Sommerville {Proc.- Roy. Soc. Edinb. , vol. xxxiv. 1914) gives a 

 description of a projection-model of the figure bounded by 

 600 congruent regular tetrahedra in space of four dimensions. 

 The volumes for 1914 and 191 5 also contain various papers on 

 determinants by Thomas Muir and by W. H. Metzler, and in 

 the volume for 191 5 Prof. E. T. Whittaker shows that the 

 functions of Lame are the solutions of a certain homogeneous 

 integral-equation. 



ASTRONOMY. By H. Spencer Jones, M.A., B.Sc, Royal Observatory, 

 Greenwich. 



Stellar Parallax Determinations. — Amongst the most remarkable 

 of the recent advances in astronomical knowledge may be placed 

 the rapid increase in the number of stars whose parallax (to 

 use a technical word) is accurately known. The parallax of 

 a star is the small angle by which it appears to be displaced 

 from its mean position, due to the motion of the Earth in its 

 orbit ; and if this angle can be accurately measured the distance 

 of a star can be calculated, since the radius of the Earth's orbit 

 is known. A knowledge of the parallax of a star is of great 

 value, because it enables the proper motion, or apparent angular 

 motion of the star in the sky, to be converted into an actual 

 velocity of so many kilometres per second, and also its apparent 

 brightness to be converted into an intrinsic luminosity relative 

 to the Sun. The difficulty of the determination of stellar 

 parallaxes lies in the fact that the stars are at such immense 

 distances, that the angle to be measured is extremely small — of 

 the order of a few hundredths or thousandths of a second of arc, 

 a second of arc being very nearly equal to the angle subtended 

 by a halfpenny at a distance of three miles. Very careful pre- 



