i6 



NATURE 



[September 2, 1915 



mathematics instruction," Prof. Franklin also raises 

 certain objections to the syllabus definition of differ- 

 entials, but we are sorry to see that he himself per- 

 petuates the worst defects of our text-books by ex- 

 panding- series of powers of differentials. It is, of 

 course, possible to expand f(x+dx)-f{x) in powers of 

 dx, and when the result is divided by dx the limit 

 of the series does happen to be equal to the differ- 

 ential coefficient in most cases, but the differential co- 

 efficient cannot be defined as the limit of the series 

 in question. It would be equally legitimate to expand 

 f{x)-f{x-dx) or f{x+^dx)-f{x — idx). The notion 

 of a differential coefficient depends essentially on the 

 assumption that the ratio of f{x2) — f{xi) to x^-Xi 

 tends to a unique limit when x^ and Xi both tend to 

 the same finite limit x. Further, we think it would 

 be much better to follow Newton's example by defining 

 equality of differentials instead of trying to define the 

 differentials themselves. The student who is taught 

 always to add dx on to the end of x fails to grasp 

 the very foundation of the calculus. The failing 

 cases may be exemplified by "density" at a point on 

 the surface separating two media. 



We have pleasure in directing attention to the little 

 volume entitled "Manchester in 1915," which has been 

 issued (in Manchester by the University Press, and 

 in London by Messrs. Longmans and Co.) at one 

 shilling net, it being the handbook for the forthcoming 

 meeting of the British Association. While less pre- 

 tentious than many previous association handbooks, 

 it is a noteworthy production, and one which should 

 be of great service to those attending the meeting; 

 it will doubtless also appeal to many residents in and 

 adjacent to Manchester, for it contains some very 

 readable and informing articles on institutions of, and 

 matters pertaining to, the city ; thus, a brief historical 

 sketch is contributed by Prof. J. Tait; Prof. Tout 

 deals with the University, Dr. Tattersall with the 

 museum, Mr. H. Guppy with the John Rylands 

 Library, and Prof. Hickson with the Literary and 

 Philosophical Society. Mr. Spurley Hey has two 

 articles on, respectively, elementary education in Man- 

 chester, and secondary schools in Manchester, and Mr. 

 J. H. Reynolds deals with the evening-school system 

 of Manchester. In addition to the foregoing, the 

 volume is finely Illustrated by some fourteen plates — 

 one in colour. Both text and illustrations are beauti- 

 fully printed. 



The Institute of Chemistry proposes to issue a 

 special edition (limited to 100 copies) of the history of 

 the institute, 1877-19 14, and orders for it can now be 

 received. Any profit arising out of its sale will be 

 devoted to the building fund. 



Mr. W. H. Dines informs us that a mistake occurs 

 in his letter in Nature of August 12 on "The Prob- 

 able Error of the Amplitudes In a Fourier Series 

 obtained from a Given Set of Observations." The 

 passage In question should read: — "To obtain p we 



etc., instead of 



• 27r 

 write np J2 — VaSin o + jiSin—. 



p = yo sino . . . . 



NO. 2392, VOL. 96] 



OUR ASTRONOMICAL COLUMN. 

 Absolute Stellar Motions. — Meddelande No. 65, 

 from the Lunds Astronomical Observatory, gives an 

 account of an important statistical study of the dis- 

 tribution of the absolute motions of a number of 

 parallax stars which has been made by Mr. K. W. 

 Gyllenberg. After excluding parallaxes smaller than 

 0015", there remain 160 stars for which absolute velo- 

 cities can be determined. The components were cal- 

 culated for an axis "Z" pointed to the galactic pole, 

 an " H " axis in the plane of the Milky Way, whilst 

 the third " S " was directed towards the vertex found 

 for 1470 stars with known radial velocities. The 

 numerical work was curtailed by using Prof. Charller's 

 plan of dividing the sky into forty-eight compartments, 

 and using the co-ordinates of the centres for the con- 

 tained stars. Prof. Charller's units SIrlometer 

 (i Sm=io® dist. earth-sun) and Stellar-j'ear (i St. = 10* 

 years) have been used (i Sm/st. =47375 km. /sec). 

 After arranging the material according to type of 

 spectrum, five star typ>es, Ki (Arct.) to A2p (Cyg.), 

 were excluded as having excessive velocities. The 

 greatest mean velocities were found in the plane of the 

 galaxy, the "Z" components giving the smallest mean 

 value. The absolute velocities tend to increase as 

 the parallax diminishes, but the increase is more rapid 

 for the small parallaxes, probably due to the greater 

 Insecurity of these measures. Hence in the final stage 

 of the work stars having parallaxes less than 0-025" 

 were excluded. It Is concluded that the distribution 

 of the absolute velocities for the remaining 144 stars 

 Is approximately , represented by an ellipsoid of revolu- 

 tion flattened in the plane of the Milky Way, and, 

 unlike the proper motions or radial velocities, the 

 absolute motions show no principal vertex. 



The Solar Eclipse of April 17, 1912. — We have 

 received copies of two papers by Seflor P. Carrasco, of 

 the Madrid Observatory, reprinted from the Annals of 

 the Physical and Chemical Society of Spain, dealing 

 with the above eclipse. One of these papers (Ann:, 

 vol. xil., pp. 482-99, 1 9 14) gives a general description 

 of the eclipse and of the work done at Cacabelos 

 (Leon) by Senor Carrasco, who had charge of the 

 spectroscopic work in the eclipse party under Senor 

 Cos, organised by the Institute of Geography and 

 Statistics. The central line of totality. It Is estimated, 

 passed about 2700 metres south-east from the position 

 occupied at Cacabelos (3° i' 39" W., Madrid, 

 42° 35' 53" N.). The observers saw something rather 

 less than totality, but more than a mere partial phase. 

 In the second paper {Ann., vol. xlil., pp. 181-238, 

 19 15) the spectroscopic observations are discussed. The 

 prismatic camera employed had " two (?) quartz prisms 

 of 60° angle, 48 mm. in height, with an objective of 

 50 mm. aperture and 630 mm. f.l." Five exposures 

 were made in ten seconds on one plate (Agfa), 

 13 X 18 cm. Three of these spectra have been measured 

 and reduced (Cornu-Hartmann formula, Rowland's 

 solar wave-lengths, and Kayser's Hauplinien). The 

 results are given in a table of some 2000 chromo- 

 spheric lines between AA3334 and 5897. The ultra- 

 violet region to A3900 has been mapped. The conclusions 

 reached are in good accord with those now generally 

 accepted ; thus, although Fraunhofer lines are common 

 to both spectra, yet the intensities are notably distinct, 

 the larger chromospheric arcs agreeing better with the 

 spark than the arc spectrum, and the principal lines 

 of the high chromosphere correspond with the en- 

 hanced lines of Sir Norman Lockyer. 



Anomalous Dispersion in the Sun. — Last year 

 Prof. Julius, by a development of the theory of 

 anomalous dispersion, concluded that there must be 



