16 



♦ KNOWLEDGE ♦ 



[July 4, 1884. 



Ansioer. — 70n +211 -4- 15c±7t x 105, n being each a nnmber as -will 

 bring the result into the given number of 100. 

 E.g. 421. 



Eemainders. 

 3)421 



140 + 1x70= 70 



5)421 



84 + 1x21= 21 



7)421 



60 + 1x15= 15 



106 



+ 105x3 = 315 



421 

 It may interest your readers to discover the rule and prove it. 

 How the Moor discovered it may be an interesting snbjeot to specu- 

 late on. G. H. BoLLANn. 



A SHEETED GHOST. 



[1329] — I once saw a ghost — that is to say, as much of a ghost 

 as I believe anyone ever saw (notwithstanding all one may read and 

 hear) excepting, of course, nervous illusions. About the "year 1861, 

 when I was eighteen, and serving my articles, I was in bed with 

 the window-blind up, and the moon shining into the room and on to 

 my bed. I half awoke and, to my surprise, saw standing on me 

 and reaching beyond the ceiling, a tall figure, like that of a man or 

 woman draped in white. I continued to look at the figure, and 

 then not feeling comfortable, resolved to ascertain what it all 

 meant. At this time I was still only half awake, as only a few 

 seconds had elapsed. 



I raised myself, and lo ! my ghost vanished. But not quite ; for 

 in a moment the optical illusion was apparent to me. 



Just in front of and close to my eyes had been a pointed fold of 

 the upper sheet of the bedclothes, and upon this the moon shone. In 

 my half-awake condition the effect was perfect, and apparently the 

 figure stood there in all its height ; but when I moved I became 

 more awake, and saw the ghost disappear into the pointed fold of 

 the sheet. j. b. Williams. 



TRUE AND FALSE PERSPECTIVE. 



[1330]— Neither " Ros. Vansittart " [1276] nor " An Old 

 Draughtsman " [1288] appears to me to have touched the diffi- 

 culty felt by " R. Jones " [1244], which is one that I (as a teacher 

 of drawing) have found very puzzling to learners, especially to 

 those who Hke to know exactly the "why and wherefore" of the 

 rules they are taught. The fact is that the usual method, illustrated 

 ''7.".''^° *-"'' ^''^""•itsman," is a compromise between the impos- 

 sibility of drawing a picture with a movable centre of vision and 

 impractibility of drawing one on the inner surface of a sphere. 

 The point of view for each picture must be rigidly fixed, and this 

 necessitates the limiting of the field of view to a circle forming the 

 base of a cone^ whose sides meet at the eye at an angle of not more 

 than about 45° (some artists say not more than 30°). As soon as 

 the eye is dii-ected towards any other point than the centre of the 

 base of this cone, the point to which it is directed becomes at once 

 the centre of the base of a new cone, and a new picture must be drawn 

 upon that point as centre. This is the difficulty experienced by 

 ' R. Jones," and over which so many students stumble. As long 

 as the face of a cube is square to the direction of the observer's 

 eye, it must be drawn square, although it may be on one side of 

 the line of direction, for, as soon as he looks directly at it, he changes 

 the position of the centre of vision, which then falls upon the cube 

 itself, and the line of direction is no longer square to the same face 

 of the cube. 



The only exact way of representing objects as they actually 

 appear to the eye is by drawing them on the inner surface of a 

 hollow sphere to be viewed with the eye at the centre. This, of 

 course, is impracticable, and indeed is unnecessary, as the same 

 effect is got in the usual way if the visual angle is not made too 

 large. Each picture may be then considered as a circular segment 

 of a sphere of which the line of direction is a radius, and if the 

 seguieut be taken small enough it will be so nearly a plane as to be 

 represented on a flat surface without undue distortion, and when 

 viewed at the centre will give the exact effect of the real object. 



Wm. Field. 



LETTERS RECEIVED AND SHORT ANSWERS. 



John A. R. Newlands. Tou will find a sliort review of yonr 

 book on page 370 of our fifth volume. — H. A. Nesbitt. Letters by 

 the Rev. C. L. Dodgson and another correspondent were marked 

 for insertion a fortnight ago. — Ignoeaxt. Your question is more 

 diflicult to answer than it looks. I know of good books whence 

 you may learn the various wild flowers, and cheap books having 

 the same end ; but none rigidly answering both descriptions. 

 " Familiar Wild Flowers," published by Cassell & Co., and Ann 

 Pratt's " Wild Flowers," published by the Society for Promoting 

 Christian Knowledge come under the former category. Of the 

 lower-priced works Bettany's " First Lessons in Practical Botany," 

 published by MacMillan for a shilling, is as good as any. — Geoege 

 Hill wants to know how many feet of air can be compressed into 

 an iron vessel one foot square ? Obviously this must depend npon the 

 strength of the vessel ; 250 ft. it it is strong enough. Perhaps some 

 aeronautical reader will answer your question. How long it takes to 

 fill an ordinary balloon. — Feedekick Elgak. My personal experience 

 with reference te strawberries differs widely from yonrs. I have 

 eaten unnumbered gallons of there without developing either 

 rheumatism or gout; albeit both my father and grandfather 

 suffered from the last-named complaint. Should this meet the 

 eye of Mr. Mattieu Williams he may, perhaps, give yon the benefit 

 of his opinion. — JoHx Cha.nxon. While persistently declining to 

 advertise trade articles in the Health Exhibition now open at South 

 Kensington, I willingly call attention to your exhibit of a Brick 

 Finial in Class 50, representative as it is of the style and quality of 

 instruction imparted at the Technical College, Finsbury, where all 

 the real work of the City and Guilds of London Institute will be 

 done in the future, as it has been in the past. — The Yxiscedwyx 

 Company send me a pamphlet to prove that London might be 

 rendered practically smokeless by the use of anthracite, as is the 

 case in New York. — John E. Svms defends the usual method of 

 drawing a cube against "R. Jones " and " C. E. Bell " (letters 1,244 

 and 1,307). Perhaps I may suggest that each of the disputants 

 should place a cube behind, and with one face parallel to, a 

 sheet of plate-glass, and, keeping the eye rigidly fixed (say by 

 applying it to a pin-hole in a fixed card) trace the outline he sees 

 accurately on the glass, and communicate the result in as short a 

 form as possible. It will be time enough to theorise when we are 

 agreed as to our facts. — A. L. M. sends an account of an odd co- 

 incidence. He is resident in the house of an old gentleman who is 

 a keen flower-gardener. On the 19th nit., my correspondent was 

 watching his landlord smarten up his beds, and after a little 

 badinage, threatened to get up in the night and ride a donkey over 

 them ! As a matter of fact, a donkej- did wander from its house 

 that very night, get into the garden, and make an utter wreck of 

 it ; and on seeing its hoof-marks the next morning, the unfortunate 

 proprietor of the ruined flowers could at first scarcely be convinced 

 that his lodger had not carried his curiously improbable jocular 

 threat into execution. "Now," says my correspondent, "I ask, 

 suppose that I had threatened to kill him instead, and he had been 

 found dead in the morning, could I have escaped hanging?" — 

 A. P. SiN.VETT. Premising that reviews in this journal are not 

 written by its editor unless specially signed by him, but are penned 

 by contributors supposed to possess special knowledge of the 

 subjects of the books to which they relate, I regret that the writer 

 of the notice to which you take exception should have employed 

 a phrase in the slightest degree calculated to hurt yonr feelings ; 

 but having myself read your book when it first appeared, I can 

 only conceive that he said — with perhaps rather needless brusqne- 

 ness — what every impartial reader of it m.ust have thought. Yonr 

 cutting from Lijht is not worth the paper it is printed on, inas- 

 much as the citation of many of the names it contains as those of 

 Spiritu.alists is dislione-'t. Thackeray, for example, repudiated, 

 both editorially and in his private capacity, the slightest belief in 

 the cock-and-bull stories told by Robert Bell in Vol. II. of the 

 Cornhill Magazine (vide Vol. VII. of that magazine, p. 706). Lord 

 Brougham, again, publicly denied any belief in Spiritualism, and 

 so on. Professor Hare was insane, and died, I believe, in an 

 asylum. Nay, will you write to the very first man whose name 

 heads your list, the Earl of Crawford and Balcarres, asking him 

 whether he does or does not believe that so-called " Spiritual " 

 phenomena are supernatural — and publish his reply ? Mr. 

 Crookes's "Phenomena of t^piritualisra " lies on the table before 

 me as 1 write. Finding, as I do, in it its author's testimony 

 to the probity and the reality of the phenomena exhibited 

 by Miss Florrie Cook (whom he took such elaborate pains 

 not to find out), and knowing how this same Miss Cook's 

 imposture was at once detected on Jan. 9, 1880, by Sir 

 George Sitwell and Herr von Buch, what possible value 

 can 1 attach to anything that Jlr. Crookes may testify or say 

 on the subject of spiritualism? It is idle to t!k!k of "the frauds 



