226 



♦ KNOWLEDGE . 



[Sept. 12, 1884. 



revolves, each pair of spokes is brought into the position occupied 

 an instant before by another pair. If, then, the intersection of 

 two spokes gives rise to any appearance, the revolution of the 

 wheel will cause that appearance to become a continuous curved 

 line. The effect of the apparent intersection is, of coarse, to shut 

 out from sight a portion of the further spoke ; and, if the edge of 

 the latter be brightly illuminated, this occasions a very definite 

 optical effect. It is to this eclipse of the bright edge of the re- 

 moter spokes that these optical curves must be ascribed. 



The mathematical investigation of these curves is not without 

 interest, and will afford a useful exercise to the student who 

 desires to find the equation. We shall not enter into the details of 

 the work, but merely indicate some of the results at which we have 

 arrived. 



Considering the visible appearance as projected on the vertical 

 plane, it will be found that the curves traced on that plane are of 

 the fourth degree, that they are divided into two loops by the 

 perspective trace of the axle (which accounts for the change of 

 position as the machine passes the eye), and that the projections of 

 the two points from which the spokes spring are singular points on 

 the curves. Lastly, any curve of the system may be generated as 

 follows : — Given a point, a line, and a circle, the curve is the locus 

 of a point such that the product of its distances from the point 

 and line bears a constant ratio to the square of the tangent drawn 

 to the circle. A. St. John Clerke. 



THE WICKED FLEA. 



[1395] — To exterminate the pestilence that walketh as well as 

 the one that hoppeth by night, I have found nothing so efficacious 

 as to pepper the mattress finely with dry bleaching powder, which 

 is best carried in a bottle. Take care not to let any stay in lumps, 

 as it rots clothes. City Bee. 



PARKGATE. 



[1396] — Having lived at Parkgate for over two years, I beg to 

 doubt Mr. Percy Enssell's opinion (expressed in Knowledge No. 147) 

 as to the fitness of the estuary for a haven for commercial fleets. 

 Half-way across there is a large sandbank, which very, in fact 

 most, often is not covered by the tide, and consequently a fishing- 

 boat left in its neighbourhood is perfectly safe without an anchor. 



Parkgate now is far from being a watering-place, or competing 

 as such. The cause of its decay is, I believe, twofold— (1), that the 

 channel of the Dee has changed from the Parkgate to the Welsh 

 side of the estuary. (2) The obnoxious smells coming across the 

 river from the Kent chemical works. Parkgate, however, has its 

 attractions, and nothing could be pleasanter than a night's shrimp- 

 fishing in Bill Smith's boat round Hilbury Island, and never were 

 shrimps so good as those fresh from the boiling-pot on deck. 



Certainly, Parkgate, from a picturesque point of view, is unique, 

 and the old adage, " All on one side, like Parkgate," is literally 

 true, even down to the curious railway-station. P. W. T. 



LETTERS RECEIVED AND SHORT ANSWERS. 



F. CowLET. — Tour request almost amounts to one that I should 

 give you the catalogue of a small library. Toa had better get 

 Doctor Brewer's " Reader's Handbook," Lempriere's " Classical 

 Dictionary," Bohn's " Dictionary of Classical Quotations," Tod- 

 hunter's books on Trigonometry and the Differential and Integral 

 Calculus (see also lessons on the former in these columns), Cassell's 

 " Latin Grammar," Delille's " French Grammar," &c. How can 

 I possibly tell what book Mr. George Augustus Sala recommends ? 

 — C.iPTAiN D.Forbes. Many thanks; utilised elsewhere.— Scientist. 

 There is no such thing as an " art of writing with special reference 

 to scientitic work." My own experience of the caligraphy of 

 men of science induces me to imasine that it ranges from 

 moderate badness down to practical illegibility. — Berks. Your 

 informant was either a knave or a fool ; most probably the latter. — 

 QuiDAM. Every discovery of an additional three weeks' supply of 

 coal in this country possesses both popular and scientific import- 

 ance, in view of the fact that the total amount of coal-bearing 

 strata beneath these islands is limited. — Ne Sutor tltea Crepi- 

 DAM. What a pity you don't take your own motto to heart. I con- 

 gratulate you on your champion. Were I to print the author's 

 name, even you might admit that he requires no instruction in the 

 subject you refer to. — G. W. N. " Popularising Astronomy " is a 

 subject with which certainly more than one member of our staff is 

 competent to deal. — Charles Proerel. Much too metaphysical 

 for these columns. — Vega. Jevon's " Elementary Lessons in 



Logic," and " Studies in Deductive Logic," both published by 

 Macmillan & Co., ought to suit you. The best small volume on 

 elementary geology is Page's " Advanced Text-Book," published 

 by Blackwood.— Aectcrus. Kindly consult Vol. IV. of Know- 

 ledge, pp. 68, 84, 100, 116, and 139.— Harold Rowntree 

 proposes to get to the North Pole of the earth by sub- 

 marine navigation. I presume that Mr. Rowntree is aware that 

 icebergs have been seen rising between 200 ft. and 300 ft. above 

 the sea, and that something like eight times their visible mass 

 must have been submerged. Has he provided against running into 

 the base of one of these stupendous floating islands ? He will ex- 

 plain the design of his vessel to any one who may care for such 

 explanation. — Faciebat. M. Mouchot ought to win one of the 

 Tit-Bits prizes. I have not read Mr. J.'s article, and your extract 

 is not too intelligible in the absence of the context ; but, of course, 

 the tremulous motion of objects in landscape, viewed in blazing 

 sunshine, is more perceptible in the distance, because they are seen 

 through a long stratum of heated air. Every ray of the sun which 

 reaches the earth brings actinic power with it. — H. W. Pake. See 

 paragraph at the bottom of col. 1, p. 62. — R. G. Tour coincidence 

 is of much too commonplace a character to justify me in occupying 

 space with it. — George S. Gibes. I cannot reprint letters te other 

 journals.— Lekrvn. Professor Clifford died at Madeira on March 3, 

 1879. It is absolutely and utterly false that he joined the 

 Church of Rome before his death. See pp. 24, 25, and 26 of 

 Vol. I. of his "Lectures and Essays," published by Macmillan. 

 — Nemo. There is a table of semidiurnal arcs in Chambers's 

 " Mathematical Tables," by the aid of which the approximate time 

 of rising may be found of any star whose declination and time of 

 southing are given. — H. B. L. The proceedings of the Learned 

 Societies are practically all purchasable by the public, though, as a 

 rule, not in numbers, but in volumes. Single numbers, however, of 

 the Journal of the Royal Microscopical Society may be bought at 

 Williams & Norgate's, and volumes of the R.A.S. " Monthly 

 Notices" of the same publishers. I do not know the name of the 

 publishers of the Geological or Linnaean Society's transactions. — A 

 Well-Wisher (Burra-Burra, S.A.). Without reprinting an entire 

 paragraph verbatim here, I may mention that what Mr. Jago says 

 is, that alum possesses the power of arresting the action of the 

 gluten of damp flour on its starch, prevents the decomposition of 

 starch, and bread from becoming sour or mouldy. Yonr complaint 

 about numbers forwarded to the publishers. Thanks for friendly 

 expressions. — Algeexon Beay points out that the mere labour of the 

 production of a magic cube is less than is supposed (especially 

 when the root is a prime number). Letter forwarded. — H. A. B. 

 The book from which you quote is a mere compilation, destitute of 

 the slightest scientific authority. The difficulty about the Equation 

 of Time seems wholly of your own creation. On November 2 in 

 this year the Sun will south in London at lib. 43m. 41s. a.m., as 

 shown by a clock indicating Greenwich mean-time, and will set 

 there at 4h. 29m. p.m., as shown by the same clock. — Commentator. 

 Oh, good gracious ! It is related that after a Devonshire parson 

 had stated in a sermon that Commentators did not agree with him, 

 a farmer waited on him with a present of a basketful of potatoes, 

 saying, that as his spiritual pastor had intimated " that common 

 'taturs didn't agree with him, he had brought him a basket of his 

 best kidneys, which he hoped he would find more wholesome." I 

 am a little afraid that the readers of Knowledge would cry out for 

 something " more wholesome " after the few columns into which 

 your communication would print. — W. Hepwoeth Collins. The 

 writer of the letter of which you enclose a cutting is not 

 responsible for his actions, and to print it would do him 

 more harm than good. — John W. STANiroRXH is exercised about 

 the dynamics of a briar-root pipe ; which, floating on the sea 

 about half-a-dozen yards from the shore, of course bowl upwards, 

 remained sensibly in one spot, and for a quarter of an hour rotated 

 from east to west about north round its stem as an axis. Its 

 moment of inertia would of course operate in rendering the 

 direction of its motion persistent. — Dr. E. South. I cannot say oft- 

 hand who was the first person to point out the unsoundness of 

 Olbers's idea, bat each fresh discovery of an asteroid, and the 

 manner in which they are grouped, adds to the accumulated mass 

 of proof that they can never have been united in a single body. 

 Are yon aware that the nodes of their orbits lie in all parts of the 

 ecliptic ? — Arnold T. Reed. Professor Jevons was entirely correct ; 

 the moon's (so-called) "changes" have nothing to do with the 

 weather in any shape or way. If the "marble" is composed of 

 carbonate of lime, it will attract the lime in the water to itself, for 

 a pretty obvious chemical reason. The best book on electrical 

 measurement, at a moderate price, is " Kempe's " Handbook of 

 Electrical Testing." — A. G. White. I do not myself know the 

 Table of Pythagoras, and am many miles from a copy of Peacock's 

 " History of Arithmetic," in the Encyclopaidia iletropoUtana, the 

 likeliest place to find an account of it. 



