NOVKMBBR 1, 1889.] 



KNOWLEDGE 



17 



When these binomials are multiplied out, every term will 

 contain a 9, except the last of each — so that if the sum of 

 the last terms, that is the sum of the digits, happens to 

 be a multiple of 9, the whole number is so, and r/V-c ivrsa. 

 It is evident that the series of numbers corresponding to 

 the sums of the digits of successive multiples of 8 decreases 

 by steps of one at a time ; because, if we add 8 to any 

 number we usually decrease the number in the integer 

 place by 2, and add 1 to the number m the tens place, 

 which decreases the sum of the digits by 1. Wiiltiples of 8 

 never have a 1 in the last place, but the passing from 1 to 

 9 and from to 8 is really a step backwards of 2 if we 

 consider the figures to be written in a circle, or in an end- 

 less recurring series. Similarly the series of numbers 

 corresponding to the sums of the digits of successive 

 multiples of 7 decreases by steps of 2 at a time, and so on 

 till we get to multiples of 4, when the step backward is 5 

 at a time, which with groups of 9 bring you to the same 

 numbers as stepping forwards 4 at a time, and steppmg 

 backwards 6 at a time gives the same numbers as stepping 

 forwards 3 at a time. Mr. Staniforth's square shows that 

 the well-known 9 rule is only a particular case of a more 

 general law, when tlie steps of the series are at a 

 time, and as you begin with 9 you never get any further. 

 — A. C. Eanyaed.] 



DO VIPERS PROTECT THEIR YOUNG IN TIME OF DANGER 

 BY SWALLOWING THEM ? 



'I'd the KiUtur of Knowledge. 



SiK, — There still seems considerable doubt among 

 several of your correspondents concerning the correct 

 answer to the above query. Will you allow me to relate 

 my experience ? When I was a lad between tliirteen and 

 fourteen years of age I started with a party of ten or a 

 dozen l)oys from Chichester for Goodwood on a buttertiy- 

 catohing expedition. We arrived on the downs, and, after 

 very fair success in chasing and capturing insects, were 

 fain to rest our tired limbs on a log which lay just on the 

 outskirts of a plantation of pine trees. ]5oys that we were, 

 we could not sit still very long, so began to roll the log as 

 we sat on it. .Just from imder my part of the log out 

 came an adder, making, if I remember rightly, a slight 

 hissing noise, and followed by some five or six little vipers, 

 I should tliink, of about one and a-half to two inches in 

 length. The mother, as we took it to be, opened her 

 mouth, and the little ones glided instantly into it and 

 disappeared, as also did the mother, into the thick grass 

 of the adjoining scrub. — I am, yours truly, 



II. C'OMHES. 



Haverstock Hill Board School, N.W. 



THE FACE OF THE SKY FOR NOVEMBER. 



Uy IIekueut Saulek, F.U.A.S. 



THE increasing number of smispots, though no \ery 

 large ones have yet appeared, shows that the 

 mininnnu is now fairly past. Conveniently 

 oljservable minima of Algol take place on the 1st 

 at 7h. 58ni. p.m., on the 4th at 4h. 42m. p.m., on 

 the 21st at 9h. 35m. p.m., and on the 24th at 6h. 24m. 

 P.M. A minimum of \ Tauri occurs at .')h. .'ini. p.m. on the 

 evening of the 1st. In tliis star the change of light from 

 normal brilliancy (3-4 magnitude) to mininnnu (4-2 magni- 

 tude) and back again takes a little more than 10 hours. 

 Mercury is well situated for obser\-ation during the first 

 three weeks of the month. On tlie 1st he rises at 4h. hHin. 



A.M., or just two hours before sunrise, having a southern 

 declination of 6° 26', and an apparent diameter of 61". 

 On the 19th he rises at 6h. 24m. a.m., or rather less than 

 an hour before the sun. having a southern declination of 

 16° I", and an apparent diameter of 5". On the morning 

 of the 10th he will be about \\° s.ji. the 4th magnitude 

 star K Virginis. During the month he passes from Virgo 

 through Libra into Scorpio. Venus is a morning star, but 

 is rapidly losing her brilliancy. On the 1st she rises at 

 4h. 18m. A.M. with a southern declination of S' j', and an 

 apparent diameter of llj ' ; just y'oths of the disc being 

 illuminated. On the 30th she rises at 5h. .54m. a.m. with 

 a southern declination of 16j°, and an apparent diameter 

 of 101". On the morning of the 4th she wUl be about 

 8' f:.p. the 4i magnitude star 6 Virginis. During the month 

 she passes from Virgo into Libra. Mars is a morning star, 

 but is not a very attractive object for amateurs, as his 

 diameter at the end of the montb only subtends 5}/'. On 

 the 1st he rises at 2h. 36m. a.m., and on the 30th at 2h. 

 20m. A.M. He is in aphelion at 7h. a.m. on the 12th. On the 

 morning of the 3rd he is about 50' x.ji. /3 Virginis. During 

 the month he passes from Leo into Virgo. .Jupiter must 

 now be looked for very early in the evening near the 

 SSW. horizon, if he is to be observed at all. On the 1st 

 he sets at 7li. 30m. p.m., or three hom-s after simset, with 

 a southern declination of 23^°, and an apparent diameter 

 of 34". On the 30th he sets at 6h. 3m. p.m., or two hours 

 six minutes after sunset, with a southern decimation of 

 23° 10', and an apparent diameter of 32 J". On the evening 

 of the 13th he wUl be 14' due north of the 6th magnitude 

 star B.A.C. 6343. He is in Sagittarius throughout the 

 month. The following three phenomena of the satellites 

 occur between the times of the planet's beuig 8° above, 

 and the sun's being 8° below, the horizon on the days 

 named. On the 1st a transit egress of the shadow of the 

 first satellite at 5li. 48m. p.m. On the 8th a transit 

 ingress of the shadow of the first satellite at 5h. 25m. p.m., 

 and on the lOtli an eclipse (disappearance) of the third 

 satellite at 5h. 40m. 47s. Saturn is a morning star, in 

 Leo throughout the month. Ou the Ist he rises at 

 Oh. 30m. A.M., havmg a northern declination of 11° 55', 

 and an apparent diameter of 15i". On the 30th he rises 

 at lOh. 40m. p.ji., having a northern declination of ll.i°, 

 and an apparent diameter of 16}". Marth points out that 

 on November 1st, at 8h. p.m., the satellite .Japetus passes 

 within 3" of Titan, and shortly afterwards enters the 

 shadow of the ring system, fr-om whi(-h it emerges between 

 4h. and 5h. p.m. on November 2nd. Uranus is, for the 

 purposes of the amateur, practically mvisible. Neptune 

 rises on the 1st at 5li. 36m. p.m., having a northern 

 declination of 19j°, and an apparent diameter of 2j", and 

 shines as a duU 8th magnitude star. On the 30th he rises 

 at 3h. 36m. p.m. He moves slowdy to the west din-ing 

 November, and is in opposition to the sun on tlie 25th, 

 when his distance from the earth is about 2,(i.S3 millions of 

 miles. He is between u (Omega) and 43 Tauri, gradually 

 approaching the latter. November is a very favourable 

 month for shooting stars. The most marked displays are 

 the Leonids on November 13 and 14, the radiant point 

 being in K.A. lOh. Om. Decl. + 23". The radiant point 

 rises at about a (piarter past ten p.m. The Andromcdiv 

 occur on the 27tb, the radiant point being in R.A. Ih. 40m. 

 Decl. + 43°. 'fbe moon is full at 4h. 5m. p.m. on the 

 7th, enters her last quarter at 8h. 36m. p.m. on the loth, 

 is new at lb. 44m. a.m. on the 23rd. and enters her first 

 quarter at 5h. 29m. p.m. on the 29th. On the 3rd the 4J 

 magnitude star 30 Piscium will disappear at 9h. 41m. p.m. 

 at an angle of 132° from the vertex, and reappear at 

 lOh. 55m. P.M. at an angle of 317° from the vertex, and 



