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404 



NATURE 



[February 25, 1892 



The additions to the Zoological Society's Gardens during the 

 past week include a Sykes's Monkey ( Cercopithectis albigularis ? ) 

 from East Africa, presented by Mr. G. N. Wylie ; a Beatrix 

 Antelope {Oryx beatrix ? ), an Indian Gazelle [Gazella hennetti) 

 from Arabia, presented by Lieut. -Colonel Talbot ; a Goshawk 

 {Aslttr palumbarius), European, presented by Captain Noble ; 

 a Common Quail {Cottirnix communis), European, presented 

 by W. K. Purnell ; a Hybrid Goose (between Attser cinereus 

 and A. brachyrhynchus), captured in Holland, presented by 

 Mr. F. E. Blaaluw, C.M.Z.S. ; a Gould's Monitor {Varanus 

 goiildi), a Stump-tailed Lizard {Trachydosaurus rugosus) from 

 New South Wales, presented by Mr. T. Hellberg ; a Chub 

 {Leticisais cephalus), British fresh waters, presented by Mr. 

 H. E. Young ; two Yaks (Poephagus grunniens (J ? ) from 

 Tibet, three Gigantic Salamanders {Megalobatrachus maximus) 

 from Japan, deposited ; an Azara's Agouti [Dasyprocta azarce), 

 a Pucheran's Hawk {Asttirina pticherani), a Sulphury Tyrant 

 {Piiangus sulphtirahcs), two Short-winged Tyrants {Machetornis 

 rixosa) a Brown Milvago {Milvago chimango), an Orange-billed 

 Coot {Fulica leucoptera), a Cayenne Lapwing ( Vanellus cayen- 

 nensis), six Rosy-billed Ducks {Metopiana peposaca 3 tJ 3 ? ) 

 from South America, purchased; an American Bison {Bison 

 americanus i ) from North America, received in exchange ; a 

 Gayal (Bibos frontalis ? ), born in the Gardens. 



OUR ASTRONOMICAL COLUMN. 



The Solar Disturbance of 1891, June 17.— In the October 

 number of the Observatory Mr. H. H. Turner publishes an article 

 on the luminous outburst on the sun observed by M. Trouvelot on 

 June 17, and recorded in these columns on July 9. The disturbance 

 was of such an unusual character that M. Trouvelot hazarded the 

 suggestion that it was possibly accompanied by perturbations of 

 the magnetic elements. Mr. Whipple was good enough to look 

 over the Kew curves to see if they showed any such variations, 

 and a negative result was obtained. Mr. Turner, however, 

 after an examination of the Greenwich records has succeeded in 

 finding "a very minute, though unmistakable, disturbance at 

 almost precisely the time noted by Trouvelot. . . . The 

 disturbance is smaller than many others on the same day, 

 although the day itself was very quiet : but it differs from 

 others in its abruptness, which is clearly shown in all three 

 curves. The change in declination is only about 1', and in H.F, 

 0*0005 of the whole H.F." Diagrams illustrating these fluc- 

 tuations accompanied Mr. Turner's paper. It seemed strange 

 that the Kew and the Greenwich records should differ in their 

 indications, so a iurther enquiry was sent to Mr. Whipple, who 

 replied as follows : — ' ' I have again referred to the curves of June 

 17, 1891, and fail to find any trace of what can by any means 

 be termed to be a magnetic disturbance at the time in question 

 — accepting Sabine's interpretation of a magnetic disturbance 

 (see Phil. Trans, vol. cliii., p. 274), and so avoiding loose ex- 

 pressions. According to the Observatory, October 1891, 

 Father Sidgreaves is quite of our opinion as to the case in 

 point." The evidence in favour of a magnetic disturbance 

 simultaneously with Trouvelot's observation is thus not very 

 strong. 



Photography of Solar Prominences. — In a communica- 

 tion to the Paris Academy on February 8, M. Deslandres 

 described some new results obtained by him in the photography 

 of solar prominences. The object of the research was to photo- 

 graph the spectra of prominences further into the ultra-violet 

 than had previously been done. In July of last year, M. 

 Deslandres, following Prof. Hale, succeeded in photographing 

 the spectra to \ 380. He has now been able to obtain negatives 

 upon which the spectrum extends from X 410 to A. 350. In order 

 to obtain this result, a siderostat with a mirror 8 inches in 

 diameter has been employed to project the sun's image, a 

 Rowland gratirsg has been used to produce the spectra, and the 

 lenses of the observing telescope have been made of quartz. 

 The photographs show eight bright lines of the ultra-violet 

 hydrogen series, and it is believed that observations made from 

 an elevated station would lead to the detection of the remaining 

 two. The line a little more refrangible than hydrogen a (A 388), 



NO. II 65, VOL. 45I 



is also recorded upon the plates. Photographs have been taken 

 of the spectra of spots and faculse. The calcium lines at H and K 

 often appear bright upon them, and are always stronger than 

 the hydrogen lines. But no new facts appear to have been 

 discovered in this direction of work. 



On the Variation of Latitude. — Dr. S. C. Chandler 

 has published a series of papers on the variation of latitude, in 

 the Astronomical yournal hom No. 248. to No. 251. The general 

 result of a wide discussion indicates a revolution of the earth's 

 axis of inertia about that of rotation from west to east, with a 

 radius of 30 feet measured at the earth's surface, in a period of 

 427 days. 



NON-EUCLIDIAN GEOMETRY} 

 "pVERY conclusion supposes premisses ; these premisses 

 -*-^ themselves are either self-evident and have no need of 

 demonstration, or can only be established by assuming other 

 propositions ; and as we cannot continue this process to infinity, 

 every deductive science, and especially geometry, must rest on 

 a certain number of axioms which cannot be demonstrated. 

 All treatises on geometry therefore commence with the enuncia- 

 tion of these axioms. But a distinction must be made between 

 them : some — such as this for example, " Two quantities that are 

 equal to a third quantity are equal to one another" — are not 

 geometrical propositions, but are analytical ones. I regard 

 them as analytical a priori judgments, and as such I will not 

 discuss them. But I must insist on other axioms which are 

 special to geometry. Text-books for the most part state them 

 very explicitly : — 



(i) Only one straight line can be drawn between two points. 



(2) A straight line is the shortest distance between two points. 



(3) Only one straight line can be drawn through a point 

 parallel to a given straight line. 



Although the demonstration of the second of these axioms is 

 generally dispensed with, it would be possible to deduce it from 

 the other two, and from those, of which the number is more 

 considerable, that we admit explicitly without stating them, as 

 I shall explain in the sequel. 



Efforts have also for a long time been made without success 

 to demonstrate the third axiom, known under the name of the 

 postulatum d'Eticlide. The amount of trouble that has been 

 taken in that chimerical hope is truly beyond imagination. 

 Finally, at the commencement of the century, and almost 

 simultaneously, Lowatchewski and Bolyai, two men of science, 

 a Russian and Hungarian respectively, established, in an irre- 

 futable manner, that such a demonstration was impossible ; they 

 have very nearly rid us of the inventors of geometries without 

 postulates : since their time the Academy of Sciences only 

 receives annually one or two new demonstrations. 



The question was still not settled ; soon a great step was 

 made by the publication of the celebrated memoir of Riemann, 

 entitled " Ueber die Hypothesen welche der Geometric zum 

 Grunde liegen." This small treatise has inspired the majority 

 of recent works, of which I will make mention subsequently, 

 and among which must be mentioned those of Beltrami and 

 Helmholtz. 



The Geometry of Lowatchewski. — If it were possible to deduce 

 the postulatum d' Euclide from the other axioms, it would 

 evidently happen that in denying the postulate and admitting 

 the axioms, we should be led to contradictory results ; it 

 would then be impossible to base a coherent geometry on such 

 premisses. 



But this is precisely what Lowatchewski has done. He 

 supposes in the first place that — 



" Seve7'al straight lines can be drawn through a point parallel 

 to a given straight line. " 



And he moreover retains all the other axioms of Euclid. 

 From these hypotheses he deduces a series of theorems among 

 which it is impossible to detect any contradiction, and he 

 constructs a geometry the faultless logic of which is not inferior 

 to that of the Euclidian geometry. 



The theorems are, certainly, very different from those to 

 which we are accustomed, and they disconcert us a little at first. 



Thus, the sum of the angles of a triangle is always less than 

 two right angles ; and the difference between this sum and two 

 right angles is proportional to the surface of the triangle. 



' Translation of an article that appeared in the Revne Generate des 

 Sciences, No. 23, by M. H. Poincari. 



