150 



KNOWLEDGE 



[July 28, 1882. 



to cordiallT endorse the views of Kowalewsky. Indocil, in 1875, 

 although conrinced of the probabilities of evolution, I could not 

 accept the Ascidian relationship of vertcbrata. Now, however, 

 I deoiu it impossible for any candid naturalist (despite some 

 few unbolioriug opiuions) to do otherwise than to fully accept 

 Kowalewsky's views. Further acquaintance with recent work 

 will make each sceptic, as it made me, an ardent evolutionist ; 

 accepting the facts of nature, and the teachings of these facts, as the 

 only true guides to nature's meanings. As a matter of science, 1 

 consider the correspondence between the sea-quirts larva's structure 

 and that of the lancolet, to have been so fully made out, that no 

 «1oubt can bo entertained of the relationship I described in my 

 I'.iper on •• Found Links." Andrew Wilson. 



APPARENT PARADOX IX PROBABILITIES. 



[4vS7] — One of your correspondents stated, referring to some 

 mathematical work (not having the Xo. of Knowledge by me I 

 cannot give the exact reference), that if, out of a bag containing an 

 unlimited quantity of tickets, 100 -were drawni, and it was found 

 that oi) of them were marked A, 30 B, and 20 C, the chance that 

 the next ticket drawn wonld bo marked with some letter of the 



101 



102 



vif the ticket being marked A, B, and C, respectively, would be 

 10.T 

 r--," (Perhaps I do not state the fractions exactly right, but, at 



any rate, the second fraction was greater than the first. New, on 

 p. 577, you tell me that the fraction expresses the exact chance, not 

 meaning, I suppose, that both the fractions do in fact express the 

 oiact chances (for that, as your correspondent pointed out, would 

 involve a p.aradox, and a paradox in a case of this kind is an im- 

 possibility), but rather that the chances were e-xactly calculated 

 upon the theorj- erroneously assumed as the basis of the calculatiou. 

 Even so, the fact that the chances of such an event can be exactly 

 expressed in such a simple form seems to mo to be a very curious 

 one, and worthy to rank with two other undoubted facts which havo 

 always excited my admiration, namely, that the contents of a 

 sphere are exactly - of those of the containing cylinder, and that 



I hope that your articles on probabilities may one day get out ot 

 the domain of common sense and the multiplication table, and 

 jdore the (to me) nuknowu region to which this question belongs. 

 Alcebnon Bbay. 



[We do not feel free to carry our papers on probabilities beyond 

 the range they have already had ; but our correspondent can, wo 

 know, readily work out for himself the following demonstration of 

 the simpler law mentioned above, and afterwards extend the 

 reasoning to the more complex case. Let him then first show that 

 if we represent by ^(ii'), the sum l'' + 2'' + 3'' + ... to n terms, 

 then, if p white balls have boon drawn in succession out of a bag of 

 7. balliH, all either white or black, but in unknown proportion, the 

 drawn ball being replaced each time, the chance that the next ly 



trnlls drawn will be white is ...,, „, . an exact proposition. Next let 



l'" + 2'H 



n»f(ii-'') 

 im show that when i is very great ^^ — — — " " ' " — is very 



irly c^jnal to unity, an approximate proposition, only exact when 

 i-i infinite. He will then find no diilicnlty in showing that if in p 

 akcs, from an indefinito number of possible cases, the same event 



occur, the chance that it will occur i 

 -E...] 



the next 7 cases is 



AX AXT TRAGEDY. 



[•IS8]— I was reading the other day the interesting article on 

 " Honey Ant»" in j-onr journal; possibly the following anecdote 

 in crmnection with a species of ants in India may bo interesting to 

 some of your subscribers. 



I ran vouch for the fact", as they were told me by the observer 

 liim-'lf, a gentleman much interested in natural history. 



My frien I noticed one day one of t.'iis particular tribe of ants on 

 the ■■•:;'.] of :: r I 'n, and put a dab of honey in his path. The ant 

 .-i'' ' nrefully, ate away to his heart's content, and 



' ii-jmc, to return shortly with twenty or more 



1 During his absence, my friend j.urposely re- 



I' of the honey left, evidently to the aatonichmont 



and discomfitnro of tho ant who had enjoyed the feast, and 

 decidedly to tho chagrin and rage of his companions, who, after 

 apparently listening with disdain to tho arguments of their comrade 

 (us shown by tho action of his antenna) and tho strong " ant 

 language" used on tho occasion), suddenly set upon, killed, and 

 devoured their unfortunate and vainly pix)tesling brother. 



It certainly would bo an effectual method of getting rid of proved 

 human swindlers, but I should bo doubly sorry in that case to be 

 one of the " swindled." Uknkv J. Buck. 



THE DOUBLE STAR CASTOR. 

 [189]— As Mr. Herbert Sadler (tetter 170, p. 118) appears to be 

 severely exercised in his own mind with reference to my reply con- 

 cerning Castor, on p. 83, 1 may perhaps ask for half-a-dozen linos to 

 explain exactly in what sense I gave it. I said, and I repeat, that 

 Castor is not regai-dod by astronomers as a triple star ; although in 

 speakingof tho 11th mag. Star having " no physical connection with 

 tho well-known pair," I certainly expressed myself too strongly. 

 If, however, Mr. Sadler is going to insist that all stars possessing 

 a common proper motion, are double, triple, and so on, then must 

 he, to bo consistent, call ft, y, S, i and Z UrsfC Majoris a quintuple 

 star ! inasmuch as your own admirable researches, Sir, havo shown 

 that these stars are all moving together through space, a result sub- 

 sequently placed beyond cavil by tho independent testimony 

 afforded by tho Spectroscope.* The fact is that " double star," 

 " triple star," &c., are forms of expression conveying a perfectly 

 definite meaning to the telescopist, and to include stars more than 

 60" apart in either of these categories is to open tho door to very 

 ridiculous misdescription. One has only to note how t'.-.o late 

 Admiral Smyth padded his " Bedford Catalogue " with such objects, 

 to see where wo should be landed it wo followed out Mr. Sadler's 

 system to its logical conclusion. 



A Fellow of the Royal Astronomical Society. 



[I may note here a rather amusing misprint in Answers to 

 Correspondents, somewhat reminding one of tho familiar " Mary 

 Stet " story. In correcting tho proof, I substituted, for what had 

 before been the description of tho 11th mag. star, tho words "small 

 star." This was taken very literally by the compositoi-— sec p. 100, 

 Ist. col., line 7.— R. A. P.] 



A VITREOUS GLAZE FOR STONE. 



[-100] — The following account of Gataki-o Hall has been sup])Iicd 

 me by Mr. Hubert Smith, of Bridgenorth, and is an extract from 

 a note in his work, published some years ago : " Tent Life witli 

 English Gipsies in Nor\vay" : — 



"Thomas Gatakro was born 1.571, of a very old and ancient 

 family, still retaining their ancestral heritage of Gatakre in Shrop- 

 shire. The former II.1II of Gatakre was built of stone, three sides 

 of tho exterior of the mansion being entirely covered with a glaze of 

 greenish glass. It has puzzled many to account for tho method 

 by which the walls received their vitreous coating, effectually pre- 

 serving the stone from the action of the weather. The foundation 

 of a building on tho estate where the glass is supposed to have been 

 made still retains the name of the " (llass House." We have in our 

 possession some of the stone with its covering of glass, given to us 

 by one of the family. Tho roof of the mansion is said to havo been 

 supported by an enormous oak-treo turned upside down. This 

 interesting relic of former ngos was pulled down during tho last 

 century, and replaced by the i>resent large and spacious brick-built 

 Hall of tho Gat-acres of Ciat-aero. 



Mr. Hubert Smith has kindly procured mo two little samples ot 

 the above-mentioned vitreous coated stone, and I find that the 

 glaze is somewhat unevenly laid on tho surface, varying in 

 thickness from a thin film to about one-eighth ot an inch in 

 thickness. 



Tho stone used was a greyish sandstone, and may have boon 

 quarried in the neighbourhood, and was evidently well adapted to 

 withstand almost any amount of heat; and, judging from tho small 

 sjiccimens before me, a considerable degree of fire must have been 

 applied to tho surface, as that part nearest tho glaze is much 

 harder than at a depth of an inch. Mr. Hubert Smith further tells 

 me that all tho joints were also covered with the glaze. 



I trust that among your numerous scientific readers, some ono 

 may be able to suggest a solution of tho above pnzzle, which is 

 evidently a lost art, and may, if discovered, bo of some nse in 

 preserving some ot our public and jirivate buildings from further 

 decay. J- Milo-Gbiitith. 



• " Tho Universe and Coming Transits," p. 141. " Pleasant Ways 

 n Science," p. 143, Ac. 



