172 



- KNOWLEDGE ♦ 



[Sept. 14, 1883. 



been thrown five times running — and this is the very case with 

 which Mr. Proctor is dealing — the odds against ' size ' i-ecurring on 

 the sixth cast are not five to one, but forty-six thousand six 

 hundred and fifty-six to one. This is so bold a challenge of Mr. 

 Proctor's accuracy that wo hasten to shelter ourselves under the 

 authority of Jolm Stuart Mill, in whose ' Logic ' (Vol. II., page 75, 

 7th edition) the principle for which we are contending is laid down. 

 For the rest, Mr. Proctor's article is well worth reading; all 

 the more, on account of the high moral tone which pervades it." 



Well, the only fault here is that the critic, whom I 

 suppose to be a little inexperienced, generalises from a 

 single observation, asserting general inaccuracy on the 

 strength of a single slip (as he supposes my use of the 

 word " verbiage " to be). As to this word, which was first 

 used (and invented) by Samuel Johnson, it is commonly 

 defined, I know, as meaning merely "wordiness." Johnson 

 himself did not use it in that sense. If he had meant 

 " wordiness " he would have used the older word " ver- 

 bosity." My critic evidently thinks " verbosity " and 

 " verbiage " the same, as many do who ought to know 

 better — some dictionary-makers to wit. I prefer "to use 

 the word as a more convenient form than " terminology " 

 or " nomenclature." Besides it chanced (a mere detail) 

 that I did not mp.an terminology or nomenclature. " Slang" 

 would not have suited me at all. A word so recently in- 

 troduced into our language as " verbiage " is not quite so 

 definitely fixed in meaning as my critic imagines, nor to be 

 too readily made identical with another much older word 

 ("verbosity") the existence of which is enough to show 

 that " verbiage " as used by Johnson (who knew all about 

 verbosity) had a different significance. 



As for the " gross fallacy," — if John Stuart Mill has in 

 his " Logic " said that the chance of throwing " size " after 

 " size " has been, and is known to have been, already 

 thrown five times running, is 46,656 to 1, that would only 

 illustrate the fact, already known, that Mill's mathematical 

 conceptions were inexact. The odds are not even 16,656 

 to 1, but -16,655 to 1 against throwing "size" six times 

 running. But to make the odds the same against throwing 

 a sixth " size " after five already thrown, as they are 

 against throwing " size " six times running, would be so 

 gross and palpable a blunder, that I cannot imagine Mill 

 ever imagined it. It is hardly necessary for me to point 

 out that my own statement simply presents the truth as 

 known to every mathematician. But I think 1 can make 

 the fallacy attributed to ilr. Mill quite clear to my critic. 

 Suppose, in coLn-tossing, " head " tossed three times 

 running. According to the view I have presented, 

 the chance of tossing a fourth " head " is simply 

 one half, or the odds for and against are even 

 (1 to 1). According to the view attributed to Mill, 

 as four heads come in succession in only one case out 

 of 16 possible cases, the chance is 1-16, or (making 

 the same confusion between the chance and the odds), my 

 critic would write that the odds are 16 to 1 (instead of 15 

 to 1, as they would be if the chance is 1 in 16). But 

 half-an-hour's steady tossing will soon convince my critic 

 in Life that this is not the case. He will get, perhaps, 

 fifty or sixty cases in which heads or tails come three times 

 at least in succession, and he will find that in about half 

 {not in about a sixteenth) of these cases head or tail, as 

 the case may be, is tossed a fourth time. If he would lay 

 a wager of £15 to £1, after every case in which three 

 heads or three tails had appeared, that the fourth tossing 

 would not be of the same kind as the three, his opponent 

 would very soon be able to say of the problem — as my critic 

 retreated from before him with empty pockets — Solvitur 

 ambnlando ! 



But my critic in Life speaks with becoming modesty on 

 a subject which — as he seems to admit — he has not very 

 carefully studied. Where we chiefly differ is in this, — I 

 have carefully studied it. 



As regards " accurate knowledge of my native tongue " 

 (a most inaccurate expression, by the way), I think I may 

 say to my not unkindly critic, — 



Teach not a parent's parent to extract 



The embi'yo juices of an egg by suction ; 

 The good old lady can the feat enact 



Quite irrespective of your kind instruction. 



THE FACE OF THE SKY. 



Feom Sept. 14 to Sept. 28. 

 By F.R.A.S. 



THE student will continue to watch the Sun daily for signs of 

 disturbance. Splendid faculaj appear now at intervals on 

 tlie solar limb. The face of the stellar vault will be found deh- 

 neated on Map IX. of " The Stars in theii- Seasons." Mercury is 

 an evening star, but is very close indeed to the horizon at sunset. 

 As Venus comes into superior conjunction with the Sun on the 

 20th (in other words, is behind him), it is needless to say that she 

 will be invisible during the rest fourteen days. Mars rises soon 

 after 11 o'clock at night on tl:o 14th, and between 10 and 11 p.m. 

 by the 28th, half-way between the X.E. and the X.E. by E. 

 points of the horizon. His diameter is slowly increasing, but 

 little or no detail can as yet be made out upon his suface with the 

 telescope. Jupiter rises at half-past 12 o'clock at night on the 

 14th, and before midnight by the end of September. His path lies 

 in Cancer during our specified period. ]S"o fairly observable 

 phenomenon of his satellites occurs during the ordinary working 

 hours of the student's night. Although Saturn is on the meridian 

 during the early morning, yet he rises about 9h. 7 in. p.m. on 

 the 14th, and soon after 8 h. iu the evening of the 28th. With 

 his rings approaching their greatest opening, the planet now pre- 

 sents a spectacle of the highest interest to the observer with 

 the telescope ; and is coming into a more favourable position 

 every night. He is above and a little to the left of Aldebaran. 

 Uranus, like Venus, is behind the stin, and, of course, invisible. 

 Xeptune in a barren point of Aries is indistinguishable from a tele- 

 scopic star. The moon is 12"9 days old at noon on September 14, 

 and, quite obviously, 26'9 days old at the same hour on the 28th. 

 The full moon of the 16th is the so-called " Harvest Moon." 

 After the 23rd, she rises too late for the ordinary amateur observer. 

 Occultations of stars \sj the moon are rather more numerous during 

 the next fortnight. Of those which occur not much later than 

 midnight we may mention that of c' Capricorni, a 4i mag. star, which 

 will disappear at Sh. 44m. p.m. on September 14, at the moon's 

 dark limb, at an angle from her vertex of 171^" ; reappearing at her 

 bright limb, at a vertical angle of 208', at f'h. 5m. p.m. On the 

 same night c- Capricorni, [a 6th mag. star, will disappear at the dark 

 limb at 8h. 47m. at a vertical angle of 91°; and reappear at the 

 bright limb of the moon at lOh. p.m., at an angle of 300° from her 

 vertex. Passing over occultations which happen at 3h. 4m. and 



5 a.m., we come to one of the 6th mag. star B.A.C. 1,110 which on 

 the night of the 20th will disappear at the moon's bright limb at 

 llh. 47m. at an angle of 7 from her vertex to reappear at the dark 

 limb, at an angle from the vertex of 308°, 20 minutes after 

 midnight. Before the moon rises on the 22nd she will 

 have occulted 120 Tauri, a 6th mag. star. Subsequently 

 this wiU reappear from behind her dark limb at lOh. 

 19 m. p.m. at an angle of 239' from her vertex. Lastly, on the 

 24th, 27 minutes after midnight, 68 Geminornm, a star of the X>k 

 magnitude, will disappear at the bright limb of the moon, at an 

 angle of 30" from her vertex, to reappear at her dark limb at a 

 vertical angle of 243^ at 1 h. 19 m. the next morning. The moon 

 occupies all to-day and a great deal of to-morrow in traversing 

 Aquarius, passing into Pisces about 5 a.m. on Sunday, the 16th. 

 It is 4 a.m. on the 19th before she has performed her path across 

 this great constellation and entered Aries. She travels across 

 Aries until 7 p.m. on the 20th, when she passes into the confines 

 of Taurus, her passage across which takes until 6 a.m. on the 23rd. 

 At this hour she enters the northern boundary of Orion, which she 

 occupies twelve hours in crossing, emerging into Gemini about 



6 p.m. At noon on the 25th she enters Cancer, which she quits for 

 Leo between 5 and 6 o'clock in the morning on the 27th. At 

 midnight on that day she descends into Sextans. We there leave 

 her. 



