No-. 18, 1881.] 



KNOWLEDGE 



55 



Ifttn-g to tl)c (Btiitot, 



IThe Editor dot* not hoU himself regpomible for thf opinions of hit cot'rgfpondenfa. 

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 requests thai all commuuicatioiis thonld be a* nhorl as possible, consisfentlt/ tcith full 

 Uttd clear statements qf the writer's meaning.] 



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 Queen-street, W.C. 



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 correspondents, vhen r^erriitg to any letter, will oblige by mentioning its 7iumber 

 and the page on which it appears. 



All Letters or Queries to the Editor which require attention in the current issue of 

 Kvo-WLSnos, should reach the Publishing Office not later than the Saturday preceding 

 the day <f publication. _ 



iinod and despised who is not in a 

 lything more adverse to accuracy 



*' In knowledge, that man onlv is to b 



state of transition 'Kor is 



than fixity of opinion."- — Faraday. 



*' There b no harm in making a mistake, but great hann in making 

 me a man who makes no mistakes, and I will show you a man v 

 nothing."— ii>ly. ____ 



<J?Hr CoiTf^pontifnrf Columnd 



ERROR IX COMPUTING PERIPHERY OP ELLIPSE. 



[14] — Will you pardon me for pointing out a slight error on page 

 87 of Knowxedge ? 



In the reduction of the expression 



^ ^, 1 13 1 (13)» , -, 

 ^<^-4- 59-61- iW^°-^ 

 Yon give the result as 2058 in , instead of which it should be 

 20"508 in. I give the details as follows : — 



7.[l_l. 15-1. (i£)l] 

 '- 4 49 frl (49=) ^ 

 ^ ^64. (49)' -16. 49. 13- (13)'-, 



= '"t -ejrwf' ^ 



^ ^53661- 10192 -169t 

 = "r , -..,.^. J 



= 21. P0012. 



153664 

 143303 



1536(3 1 

 = 20-508. 

 The solution by logarithms gives a similar result. 

 Yours faithfully, 



WlLLUM J. Hardixg. 

 P.S. — May I suggest that the above expression may be given 

 as an example worked ont by logarithms to show their gi-eat 

 convenience ? — W. J. H. 



[Mr. Harding is quite right. Turning to my computation, I find 

 logarithm of result given correctly as 13119321, which is the 

 logarithm of 2050841. I took out the number, however, incorrectly. 

 The difference between the circumference of an ellipse having axes 

 7 and 6, and the circumference of a circle having diameter 6J, is 

 only a tenth of what I deduced, and is in fact less than the hundredth 

 of an inch. Had I taken axes less nearly equal, there would have 

 been a greater difference ; but it is only when the very irregular 

 heads are considered that the difference arising in this way can bo 

 ivorth taking into account. — Ed.] 



COMET.S. 



[15] — I have read with interest tlie article on comets. I am 

 always on the look out for astronomical news, and turned to the 

 article in question in the hope that soiiie light might be shed on the 

 physical nature and purpose of these mysterious tourists in space. 

 I have long been expecting some definite theory to be broached to 

 account for them ; some facts have been collected, but comets are 

 still, apparently, without the pale of celestial civilisation and order. 

 The connection between them and meteor streams is estabhshed. 

 Are we, then, to regard meteor streams as the condensed material of 

 comets left behind, and separated from the main body in the course 

 of its revolution rnund the sun ? If so, how is the fact accounted for 

 that spectroscopic examinations shows that comets are mainly com- 

 posed of the vapour of carbon, while the meteorites that have been 

 examined generally contain a large proportion of iron, nickel, &c. ? 



Is it possible that a flight of meteors at a great distance might pre- 

 sent the appearance of a comet ? Are comets to be regarded as 

 a primary condition of matter, to be afterwards condensed into 

 meteors, and these in turn to assist in tlie formation of new planets, 

 and the gradual increase of old ones ? I believe the theory, first 

 put forth by the editor of Knowi.kuge, that the rings of Saturn* are 

 com]io.sed of a multitude of minuto satellites, is generally accepted. 

 Would it be in accordance with that theory to go a step further, 

 and consider the riuirs to be dense meteor streams!-' and if so, 

 might they have been introduced to Saturn's system by a comet or 

 comets ? Any information on these points will, doubtless, be 

 acceptable to others besides 



One wno Wants to Know. 

 P.S. — The crape ring of Saturn was well seen here (Hastings) on 

 the evening of Nov. 6, power 250, 4j[ in. refractor. 



FIGURES OF THE CONIC SECTIONS. 



[16] — When I am studying geometry, as in Euclid, I am able to 

 describe circles of any size and in any position with compasses. 

 But in studying the geometry of the conic sections, 1 am not able to 

 make such illustrations as I want. I cannot draw the parabola or 

 the hj-perbola freehand ; nor, indeed, can I draw a satisfactory 

 ellipse in this way. But, even if I could, I want something more. 

 I want to be able to draw with exactitude a parabola, hvperbola, or 

 ellipse, as occasion may require, in any position ami of any size or 

 shape (parabolas, of course, are all of the same shape, but hy])erbolas 

 and ellipses are not). I observed a few weeks since in a back 

 number of the Enfrlit<h Mechanic what seems to me a very simple 

 and satisfactory way of drawing parabolic and hyperbolic arcs, as 

 follows : — 



For the parahola, set two straight lines AB, BC, (Fig 1) at right 

 angles to each other.and divide each into the same number of equal 

 parts in the points 12 3 4 5, join A\, .\2, A3, .44, A5, and through 



the points of division along AB draw parallels to BC. Then the 

 points p, q, r, s, t, in which the parallels through 1, 2, 3, 4, 5 meet 

 Al, A2, A3, A4, A5, lie on a parabolic arc through AC, which can 

 be swept ont as in the figure. 



For the hyperbola, set two straight lines AB, AC (Fig. 2) at right 

 angles, and from a point O ontside BAC draw through any points 

 1, 2, 3, 4 on AB, straight lines cutting AC in 1, 2, 3, 4. Through 



11, 22, 33, 44 draw parallels to AB, AC, meeting in p, q, r, s, then 

 the points A p, q, r, s lie on a hyperbolic arc which can be swept 

 out as in the figure. 



This is well, so far as it goes j but it does not meet my difficulty. 



• [The theory was first advanced by the Bonds, in America, and 

 independently by Clark Maxwell, of Glasgow. — En.] 



