Januaey 16, 1903.] 



SCIENCE. 



107 



line ; and if we double the folded paper 

 upon itself (another method of halving 

 it), we have the right angle. The three 

 planes at right angles are the simplest 

 systems of a combination of these products 

 of halving. 



The speaker concluded that Euclidean 

 geometry is a construction a priori of both 

 pure being and pure doing, that other 

 geometries are possible, but that no other 

 is so practical as the one which utilizes 

 the straight line, the plane, and the right 

 angle, viz., the boundaries that are con- 

 gruent with themselves. Further explana- 

 tion of his views may be expected in ar- 

 ticles to be published in the coming year. 



Evidences of Structure in the Mass of the 

 Sun: Professor Feank H. Bigelow, U. 

 S. Weather Bureau. 



This paper discussed the distribution in 

 longitude and latitude of the output of 

 solar energy as shown by the relative fre- 

 quency of the prominences, spots and facu- 

 Ise. The observations used were those 

 made in Italy by Secchi, Tacchini and 

 Ricco during the years 1872 to 1900, and 

 as they form a very regular series, the 

 annual variations are comparable and in- 

 dicate real changes in the transmission of 

 energy from the interior of the sun to the 

 outside. The result is to show that in 

 longitude there is a maximum of spots, 

 faculee and probably prominences on two 

 opposite sides of the sun, as if there exists 

 in one axial direction an excess of impulse 

 over that at right angles to it. The same 

 distribution on one diameter has been de- 

 tected already in the terrestrial magnetic 

 field and in the meteorological elements. 

 In latitude it is shown clearly that, on re- 

 covering from a quiescent state at mini- 

 mum output, the new outpouring of en- 

 ergy takes place in middle latitudes, 25° 

 to 50°, and during the increase spreads in 

 two crests, one towards the equator and 



one towards the poles, the former dying 

 away near the equator and the latter in 

 about latitude 60°. The connection that 

 probably exists between this phenomenon 

 and the Helmholtz-Emden distribution of 

 heat curves in the interior of the sun indi- 

 cates a very important type of circulation 

 which may prove to be characteristic of 

 the sun. Incidentally, the paper discussed 

 the rotation period in different latitudes, 

 and the application of the periodgram to 

 such a problem. 



Spectrographic Proof of the Rotations of 

 the Planets Jupiter, Saturn and Venus: 

 Peecival Lowell, Director, Lowell Ob- 

 servatory. 

 Eead by title. 



The Teaching of Geometry: Professor 

 Geoege Beuce Halsted, Austin, Texas. 

 Of late, very remarkable discoveries 

 have been made in geometry, affecting its 

 very foundations. These discoveries have 

 a noteworthy application to the teaching 

 of geometry. Some of these discoveries 

 and applications are considered in abstract 

 as follows: (1) The time has come for ad- 

 vance, ^(2) need for a preliminary course, 

 (3) the preliminary must fit the rational 

 geometry, (4) rigor gives simplicity, (5) 

 Euclid's unannounced assumptions, (6) 

 the betweenness assumptions, (7) superpo- 

 sition, (8) congruence and symmetry, (9) 

 the real beginnings, (10) the definition of 

 straight as shortest, (11) double import of 

 problems, (12) use of figures, (13) graph- 

 ics, (14) necessity for non-Euclidean geom- 

 etry, and (15) adaptation to teaching. 



Special Periodic Solutions of the Prohlem 

 of n Bodies: Professor E. 0. Lovett, 

 Princeton University. 

 This note constructs analytically the par- 

 ticular solutions of Lehmann-Filhes in the 

 problem of n bodies analogous to those of 

 Lagrange in the classic three-body problem. 



