September 5, 1895J 



NA TURE 



437 



passed about three-fifths of its star life, and that we cannot 

 be far wrong in assuming for the past a maximum duration 

 of about ten million years, and a radiation in the white- 

 star stage twice as intense as at present. As a step 

 towards the reconciliation of the life assigned to the sun 

 by physicists and that demanded by geologists, it is sug- 

 gested that in consequence of the higher temperature 

 when the sun was a white star, denudation was carried on 

 more vigorously, and animal and vegetable life developed 

 more rapidly than has been supposed. 



Notwithstanding that the author has approached the 

 subject with an enlightened mind, he does not appear to 

 have greatly advanced the e.xplanation. For the production 

 of changes other than those due to the progressive cooling 

 of the sun, it is necessary to suppose that the sun is sub- 

 ject to periodical changes, and the chief argument brought 

 forward in favour of this supposition is that the acknow- 

 ledged eleven-yearly period of the sun renders it probable 

 that there may also be periods of longer duration. 



It is clear that such long-period changes are quite out- 

 side our range of observation, and the indirect evidence 

 brought forward is unconvincing. We do know, how- 

 ever, that the variation which has been obser\ed in stars 

 resembling the sun is verj- rare and always slight. 



Methodisches Lehrbuch der Elemejitar-Mathen,atik. \on 



Dr. Gustav Holzmiiller. (Leipzig : Teubner, 1894-5.) 

 This is a te.\t-book of elementary mathematics, showing 

 the extent of knowledge required of the German school- 

 boy ; and apart from the interesting presentation of the 

 subjects in a manner far superior to anything we can 

 show, the book is well worthy of translation as illustrating 

 the difference in the standards of requirement of German 

 and English schools ; the knowledge exacted of the 

 German schoolboy being about the equivalent of our B.A. 

 requirements. 



But then the German schoolmaster, although working 

 to a much higher standard, can take his responsibilities 

 lightly ; he has merely to point out to his pupils that it 

 depends entirely upon themselves whether they are to 

 spend three years or only one under the civilising in- 

 fluence of the drill-sergeant. 



The harder his pupils work, to escape with one year 

 of military service, the higher the standard which the 

 government inspector can exact for exemption ; thus the 

 parado.xical result is attained that the system of con- 

 scription tends ultimately to elevate the intellectual 

 standard of school knowledge ; but, on the other hand, 

 the physical development of youth runs great risk of 

 being stunted. Obviously there is no place in a German 

 school, or French school either now, for the cricket, 

 rowing, and football, which we now consider of equal 

 importance with abstract studies. .All Europe is now 

 an armed camp, this countr>' excepted ; and the ob- 

 servant philosopher is doubtless beginning to draw in- 

 ferences as to the comparative effect of the systems on 

 the development of the human race. 



Dr. Holzmiiller's " Einflihrung in die Theorie der 

 isozonalen X'erwandschaften und der Conformen .Abbil- 

 dungen," 1S82, is a well-known standard work, profusely 

 illustrated with carefully-drawn diagrams, which em- 

 phasise many delicate points in the Theory of Functions 

 in a manner much more convincing than arguments 

 depending on a procession of analytical formulas ; so 

 also in this "Methodisches Lehrbuch," a plentiful supply 

 of figures serves as a substitute for long algebraical calcu- 

 lations. 



The author has made these elementary parts of mathe- 

 matics more interesting and pleasant reading by historical 

 notes and simple applications ; and altogether the work 

 is a great contrast to the dry bones we are accustomed 

 to here ; it would be well for our writers of school books 

 to study the sentiment expressed in Dr. Holzmiiller's 

 preface : " Uns von der allzustarren Gebundenheit der 

 Lehrpliine zu befreien." G. 



NO. I 3:J9, VOL, 52] 



LETTERS TO THE EDITOR. 



[ The Editor does not hold himself responsible for opinions ex- 

 pressed by his correspondents. Neither can he undertake 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part of NATURE. 

 No notice is taken of anonymous communications.^ 



Heights of August Meteors. 



Ln addition to the four or five meteors recorded last week in 

 Nature (vol. Hi. p. 395-6), by Mr. Denning, as having been 

 simultaneously observed at more than one station during this 

 years -Vugusi-nieteor period, particulars which have just now 

 reached nie of some observations of the Perseids made at Tring, 

 in Herts, on the night of the nth inst., show that two of the 

 meteors seen and mapped here between 9.45 and 12 p.-M. on 

 that night, also had their apparent paths mapped simultaneously 

 at a place at Tring, about nineteen miles due north from this 

 point of obserxation. The base-line between the two stations is 

 a rather short one for such comparative determinations, but as 

 the recorded flights passed nearly overhead, and nearly from 

 east to west across the line between the stations, the conditions 

 for accuracy were very favourable in both the meteors' cases, and 

 the apparent paths seem also, by the comparison, to have been 

 mapped with much precision. They require, however, as usual, 

 corrections of a few degrees at the beginning and end points to 

 make them quite geometrically compatible. 



Tring. — August II, 9.53 I'. .\i. ; 1st magn. ; left a long streak 

 along a long path ; 33", from 332* -(- 39 to 287* + 424 ; 

 (corrected path, 35°, from 32S ■¥ 40 to 280 -I- 41). Duration, 

 2 or 3 seconds. 



Slough. — August II, 9.53 r..M. ; 1st magn., white; 37° in 

 I '2 second, from 331 -f 53 to 26S -)- 51 ; (corrected path, 35% 

 from 336 -r 5oi to 277 + 54). Left a bright white streak on its 

 whole course for 3 seconds. 



The observed tracks are 15° to 13° apart, nearly parallel, but 

 slightly converging ; and if made parallel, about 14" apart 

 throughout, they indicate a radiant-point at the east-horizon 

 (11° N. from E.), at 21 -i- 7, near /i and PLscium, from very 

 near which radiant-point the meteor was, no doubt, directed, as 

 its long streak-leaving flight plainly enough denoted a very 

 nearly horizontal motion. The resulting real path is from 77 

 miles over a point 4 miles north of Farringdon, in Oxfordshire, 

 to 77 miles over a spot 3 miles E.N.E. from Uxbridge, in 

 Middlesex. This course of 50 miles, with a duration of l"2 

 seconds, gives the speed of flight 413 miles per second, thespeed 

 for meteors with parabolic motion from the same radiant-point 

 (omitting a small addition for the earth's attraction) being 40J 

 miles per second. In Mr. Greg's" General Comparative Table 

 of Radiant Positions," as No. 106 of the list (" Briti.sh Associa- 

 tion Report,"' 1874, p. },l},'), a place at 22 4- 5 is given as the 

 average radiant-centre of a group of several meteor showers 

 observed by Schmidt, in Athens (p. 321-2 of the same 

 '■ Report"), in July, August, and September. It was thus from 

 a very central direction of a rather notable autumnal group of 

 meteor-showers in the neighbourhood of a Piscium, that this 

 bright streak-leaving meteor seems to have proceeded. The 

 corrections above applied to the recorded paths, although ap- 

 jjarently considerable, are really only slight shiftings of the flights 

 lengthwise ; their original lines of direction, and hence their 

 resulting radiant-point being left, as nearly equally as possible in 

 both the paths, almost unaltered. ' 



Tring. — 11.3 i'..\i. ; shot 12°, leaving a streak, from 345 -i- 58 

 to 325 -t- 53 (corrected path, 13°, from 343 + 58 to 322 + 52). 



Slough. — 1 1.4 P.M. ; 3rd magn. ; shot 10°, without streak, 

 from 350 -f 72 to 312 + 70 (corrected path, 10°, from 352 + 72 

 to 317 + 70A). 



The path corrections here are only small shortenings or 

 extensions of the apiMrent tracks to bring their lengths into 

 agreement (at distances apart then of 13' to iS°, in the right 

 directions) without disturbing the path-directions, which diverge 

 from 45 -f 53, a |K)int nearly coinciding with the usual radiant- 

 point of the Perseids on August lo-ii, at 44-t-56. 



The concluded real path is from 67 miles over a point 5 miles 

 west of Leighton, in Bedfordshire, to 53 miles over a point 3 miles 

 west by north from Tring. The length and downward slope of 

 the real path w.is ig.J miles, from 45° altitude, 34° north from 

 east. The lime of flight of this small Perseid was not noted at 

 either place of observation, but as it probably agreed With that 

 of several similar short Perseids noted nearly overhead on the 



