October 1, 1886.] 



♦ KNOW^LEDGE ♦ 



5G1 



is liable to attract attention. On pq take a point o nearer 

 to ;) than to q, and instead of the lines KeL and fea, join 

 this point o with the points f, a, k, and l. The error in 

 the drawing will not he noticeable, and on fitting the four 

 pieces together all the spaces around e will be four-cornered, 

 and will seem to be squares. In like manner, with the 

 other triangle having E(/ as a .side. Representing this on 

 an enlarged scale, as in fig. 3 by Ejrre, and letting )• be the 

 middle point of zg, and rs a part of the line from r to b 



A/ 3 



in fig. 1, we take t on rs as a point to be connected with 

 A, F, k, and I. 



The point o should divide j>q, so that po : oq : -.fe to Ke 

 (fig. 1), or :: 5 : 2. For then the devLations of the lines 

 fromy'and K will be best distributed to escape attention. 

 But /may be slightly shifted towards a, and k towards B, 

 a towards h, and l towards d (still more slightly), to help 

 the illusion. Con-esponding remarks apply to the point t 

 and lines from it. 



When such precautions are taken the rectangle bd6c may 

 be di-a\vn very accurately, and all on a large scale, while the 

 pieces may be left for thorough inspection and repeated 

 adjustment without any chance of the trick being detected, 

 even by measurement. Of coui-se, even a lad with geo- 

 metrical proclivities will detect the trick by reasoning. 



MINUTE WRITING. 



FRIENDLY rivalry in minute writing 

 sprang up I'ecently among various corre- 

 spondents of the Xevcastle Wechhj Chronicle. 

 Someone bad written the Lord's Prayer 

 (with the Doxology, as in all cases men- 

 tioned later) within a space which a three- 

 ])enny piece will cover. Then others wrote 

 it smaller. At last, one wrote it within the space covered 

 by the end of an ordinary pencil. On hearing of this, re- 

 membering that, when a lad, I had been able to write I'ather 

 small, I tried my hand, and managed to get the Praj'er 

 into a space just over the half of that which the end 

 of a lead pencil will cover. Not to be beaten, one of the 

 small-writing company wrote the Prayer just within the half 

 of a pencil end, though, as the editor of the We.ekli/ Chronicle 

 announced, not quite so distinctly as I had written it in a 

 somewhat larger space. 



I then tried my hand again, having noticed that at each 

 fresh trial I seemed U) recover more of the skill I had 

 formerly had in such small work. The result is thus 

 described by my friend, the editor of the Xeivcnsile Weekly 

 Chronicle, who has been a sort of umpire or referee in this 

 minute contest. (I trust no reader of Knowledge, after 

 reading what follows, will assert that I have been making 

 little of the Lord's Prayer.) 



" Mr. Proctor, who is on a visit to Missouri, United 

 States, has sent me three other specimens of his skill in 

 microscopic writing. One of them is the Lord's Prayer 

 written in less than a half-ring marked by a penholder 

 smaller than an ordinary pencil-ring. Another is the same 

 prayer occupying a space slightly over the half-iing. A few 

 touches of the pen have given the latter specimen the 



appearance of tlie sun rising out of the sea. The third 

 specimen is in some respects the most striking and curious 

 of the three. It is the Lord's Prayer written three times 

 over on tliree straight lines a shade over two and a half 

 inches long. The writing in tliLs case is so straight and 

 minute that the three lines look to the naked eye like three 

 ruled lines. And yet, when placed under a magnifying 

 glass, every word is seen to be perfectly distinct. Mr. 

 Proctor's feats are perhaps all the more remarkable 

 since they were performed under trying circumsfcinces — 

 when he was, as he states, ' roasting at St. Joseph with the 

 thermometer at 107° in the shade.' " 



I expect some of the others will get ahead of this, and, if 

 so, I shall try yet again, in more favourable weather than 

 we have yet had in St. Joseph for work of this sort. 



PHOTOGRAPH OF SATURN. 



SIHE accompanying enlargement of a photo- 

 graph of Saturn, by MM. Henry at Paris, 

 like the photogi-ajihs of star-fields in pre- 

 ceding numbers of Knowledge, has received 

 no touch from the hand of an_v human 

 engraver. It is Saturn's own work. In 

 that sen.se it is full of promise. Nest month 



we hope to introduce a photogr.aphic engraving of Jupiter, 



by Jupiter. 



SATuns Self Piiotogkapiied. 



FIFTEEN SCHOOL-GIRLS. 



CORRESPONDENT asks for a solution of 

 the problem of the fifteen school girls who 

 — to avoid plots against the peace of the 

 community (of which school-boys would 

 naturally be innocent) — were to walk day 

 .after daj' in sets of three, in such a, way 

 that no two would be in the .same .set more 

 than once in seven days. Solutions will be 



found in Volume II., and a di-scussion of the puzzle there 



and in Volume III. We will give the solution next month, 



when we may also consider the general principles involved 



in such puzzles. 



There is a pu7.zle of the kind, by no means so easy as 



many might imagine, which is of frequent occurrence in a 



pi-actical way : — 



Given 2;; chess players ; how are they to be arranged in 



pairs so that there may be (2n — 1) sittings, each of n games, 



all the players being engaged at each sitting 1 



By beginning with an easy problem of pairs, problems 



relating to sets of three, four, and more may be readily dealt 



with. 



