Dec. 21, 1883.] 



♦ KNOWLEDGE ♦ 



381 



by another subordinate (call him Brown), serving in another de- 

 partment on the island, enclosed in a letter from his son in England. 

 The adyentures of the note then came out. Timothy, being a 

 liireful man, had pnt the note in an ordinary official envelope, 

 lieaded " On Her M.ajesty's Service," and deposited both in his 

 pocket. In delivering his letters at one of the offices on the main- 

 land he had drawn out the envelope containing the note, which 

 Muttered to the floor, and lay there for some time unobserved. 

 The office-keeper, in cleaning out the office next morning, 

 picked up the envelope, and seeing it was an unused one 

 placed it in the stationery -rack with others of the same sort. 

 Hrown, who represented this office on the island, found in time 

 I hat his stationery had run out, and sent over to the head office 

 for more. A supply was made up, and included the identical 

 envelope which still faithfully guarded the note. .Subsequently 

 iirown had occasion tr, write to his son, and not having a private 

 envelope at hand took an official one, picking out the one in which 

 •he note still lay undiscovered. The son on opening the letter 

 found the note, and, being an honest lad, returned it to his father. 

 The points that strike one as remarkable in this incident are — 1. 

 That the envelope should hare been dropped by Timothy without 

 :niy one noticing it. 2. That it should lie unobserved til! found by 

 the office-keeper. 3. That he should not have looked into it. 4. 

 Tliat it should have gone back to the island. 5. That Brown 

 should have used it for a letter going to England. 0. And that 

 he should not have discovered the note. I may add that the note 

 must have had hundreds of escapes from falling into dishonest 

 hands. C. A. E. 



[1061] — Your article on coincidences reminds me of one which 

 you may be glad to add to your list. It is striking, literally, to say 

 the least. 



An uncle of mine was a rather fine amateur painter, and as he 

 always presented his pictures in handsome frames, his gifts were 

 usually very acceptable. <.)ne of them went to the country, I need 

 not say where, but miles away from the town in which he lived, 

 and was placed in the gentleman's drawing-room, which happened 

 to be over the dining-room. One day whilst at luncheon the 

 family were aroused from their meal by a tremendous report of a 

 falling body in the room above, immediately followed by the crash- 

 ing of glass. Hastily rushing upstairs into the drawing-room, they 

 found the picture had fallen in such a peculiar manner as to 

 scarcely injure the lower part of the frame, but to utterly smash 

 — more especially in one spot — the uppermost portion. The owner 

 remarked to his wife how strange the picture should have thus 

 fallen to cause so strange a fracture, and added he hoped nothing 

 could have happened to the donor, which idea was laughed at by 



others present That day, and that hour, and as near 



that minute, my uncle fell down in a fit in the street, not injuring 

 his feet or legs, but striking the curbstone, fractured the skin of 

 his head, and well-nigh his frontal bone — he died at once. 



Another F.R.A.S. Subscriber. 



SILENT LIGHTNING. 



[1062]— With reference to letter 1003, p. 308, in the evening of 

 .lune 29 last I watched the path of a heavy thunderstorm from 

 S.VV. to N.E., which at its nearest point was about ten miles 

 distant. As the thundercloud covered a large area, and the light- 

 ning was at diffen'nt points, I was unable to estimate the exact 

 limit of audible thunder, but at 8 p.m., and for ten minutes later, 

 the thunder of every flash was distinct, and I judged the limit 

 roughly at fifteen miles. The wind here was light, from S.W. 

 The lightning was seen, as is frequently the case here, long after 

 the thunder ceased to be heard. The direction and force of the 

 wind seem to affect the di.stanco of hearing. 



Rectory, WorcesfiT. F. S. L. 



SILENT LIGHTMNt;.— Lr.MlNOSITY OF ANIMALS. 



[1063]. — I have met with two remarkable instances of long- 

 continued 1 yhtning, unaccompanied by thunder. Once, at Shanghai, 

 in July, the sky was illuminated with one incessant unintermittent 

 glare, lasting several hours, but no thunder was lieard. But the 

 most remarkable instance occurred in May, off the south-coast of 

 Madagascar, when, from 7 to 11 )).m., I watched a glare, which 

 left the sky dark only for a second once in an hour or so, the central 

 point of which seemed elevated 10° or 15° above the horizon. As 

 the nearer clouds cleared away, I watched for hours the unceasing 

 (lashes, tongues of fire d.nrting out round the distant clouds, ra- 

 diating in five or six distinct streams of flame from a given point, 

 like the thunderbolt in the hand of Jove, coursing along the sky, or 

 •lashing down into (he se!', at the hori/on like liquid fire; yet all the 



while not a sound was heard. After I had retired, at 11, I still 

 saw, as long as I lay awake, the reflection plaving upon the walls 

 of the cabin as from a flickering lamp. The day following was 

 marked by a brilliancy of atmosphere and freshness of temperature 

 not before experienced. On this, and another occasion at Sarawak, 

 the lightning was unusually vivid, but the flashes were not simple 

 instantaneous sparks, but had the appearance of liquid fire poured 

 from a vessel in a continuous stream, and lasting a definite time, 

 during which the lightning vibrated upon the retina, the zigzag 

 form of the flash, however, being meanwhile perfectly retained. 



In my "Rambles of a Naturalist in the China Seas" may be 

 found a chapter upon the Luminosity of Animals, the result of 

 many months' continuous observation, containing also snggestions 

 as to its origin. The chapter ends with this remark : " If we were 

 called upon to specify in what classes of animals it (luminosity) 

 has been observed, we should prefer to make a converse state- 

 ment, to the effect that, with the sole exception of birds, every 

 class of animals includes representatives, which, under certain 

 circumstances and conditions, have been proved to be capable of 

 giving out light." C. Collingwood. 



FIGURE MAGIC— CURIOUS MULTIPLICATION. 

 [1064] — Taking first the case where nothing is added (letter 

 974, page 262), it is easily seen that multiplying by 3 and 3 

 and dividing by 2, 2, and 9 is equivalent to dividing by 4 



(for z — 5 — ^ = 7) which accounts for the final multiplication by 

 4 in order to arrive at the original number. The example given (in 

 which the first of the " trebled results " is odd) is rather more diffi- 

 cult to unravel. A little consideration, however, shows that the 1 

 added is subsequently multiplied by 3 and divided by 36, and the 

 resulting ^'j is discarded in the | after dividing by 9 (93^ being the 

 full quotient). It is therefore evident that after multiplying by 4 

 the result is (-^- I'.j) x 4 = 1 too little. Hence the necessity for the 

 final addition of 1. 



It follows from the rule that any similar example (i.e., with first 

 odd and then even trebled results) must have a remainder with a 

 fraction of i after dividmg by 9. From which we can infer that 

 only those numbers will yield first odd and then even trebled 



results, which, when multiplied by - — ^ — _ | =_», and increased 



bv /__!, give a remainder with a fraction of 4. Deduct- 



■^2x2x9 \~12/ ^ 

 ing the ,V the frtiction is J ; therefore the numbers which will yield 

 odd and then even results, are those which are one in excess of the 

 multiples of 4. Similar considerations will show the reason for the 

 cases in which 2 and 3 are to be added. 



I should like very much to learn how "' A. B." arrived at his 

 curious rule for multiplication in certain cases (letter 973). It seems 

 to have some connection with the ordinary u'orkinri of multiplica- 

 tion, as may be seen by writing down his working as follows: — 

 36585 

 53658 

 85365 

 58536 

 65853 



726,175,665 



It also seems to have a relation to the well-known fact that 

 any number whose digits, when added together, make a multiple 

 of 9 is itself divisible by 9 ; for the multijilicand and product in 

 each example are multiples of 9. Perhaps " A. B." .rir.^f invented 

 his rule, then applied it to a number of multiples of 9, picked 

 out tho.sc cases in which the product was also a multiple of 9 ; 

 divided the products by the multii)licands, and thus obtained 

 multipliers from which iie selected those which had no fractions. 

 Thus he might have taken 18, multiplied it acconiing to his mle, 

 getting 828, and dividing this by 18 ; thus arriving at 46 for the 

 multiplier. But 27, 36, &c., yield multipliers with fractions. 



Dulwich, -Vor. 5, 1883. CnA.s. E. Bell. 



LETTERS RECEIVED AND SHORT ANSWERS. 

 Henry Clark, Si hsi riber. (Truly as you say what icas the 

 g<in made of.)— T. !S. B., U. B. H. Path straightest when moon 

 iific, most curved when she is full. — R. Hill. Have read your lines 

 with much pleasure and sympathy.— U. Moi-lton, C. L. Tweed.^le. 

 F'ar too complex for treatment here. — Alex. Zeptgor A. To what 

 fighting would you invite readers I- Cr. T.wlok. Thanks. Author 

 unknown to mc. Will forward.- C. Smith. We do not send re- 

 porters to lectures. — Jc^titia Fiat. Many thanks ; but ufiv should 



