500 



• KNOWLEDGE ♦ 



[Dec. 20, 1882. 



Hero u a little >rlloKira> to comfort yon: — Major premiss, 

 Brerr »Donymoas correspomleiit is to bo mistnistod ; minor 

 premif*, Ttiis currvspondcnt ia nnonymons ; conclusion, I ^Yi^ 

 Lvtake mo to the noit. — C. R. T. Xo; Xon-oomb's account 

 >>f t>»' tiil«« i« in<v>rtv<<f ; ho has liiuiscif admittoil as much. I 



|.„— ~' ...ti.i,, . ..,. ii... culiji-ct myself. I know of no better 



t! 'lut prosontcd in Sir Edward Beckett's 



• \ :naties." — W. C.KVE TllOM.\s. I owo 



1 1 Unv the word " Dclij^ht " for " Light " 



i: '11 the Libratiou of Sensation escaped 



! I cannot imagine. It looks like an 



< . is certainly worthy of much atten- 



t ry explanation of tho ocular spectra. 



— ' calls attention to tho wave described on 



I , i|>e<J somewhat like a cono." Ho was in 



I time and hcanl of no such wave, nor can 



!.. wiive. It was bo described in a letter to 



a d;i:!i J..!!., r ;.: tlio time, and was seen of many. The account 

 muiifestly means a round-top wave diminishing in height on 

 either side of its highest part, somewhat like tho half of two 

 equal cones, connected by their bases, and divided by a horizontal 

 plane through their horizontal common axis. The description is 

 inexact, of course, but in such cases it is better to use the words 

 actually given. Tho same correspondent finds (1) most of tho buds 

 in his garden have a distinctive colour, rather pinkish, and (2) notes 

 that scales must be of a strange non-conducting material to prevent 

 the bud from acquiring the temperature of tho atmosphere in 

 the coorso of a night. But it is a question of radiation, 

 not of conduction. Wells sniiltKl when his gardener spoke of a mat 

 on sticks keeping plants under them warm ; bnt Wells found the 

 gnnlcnerwos right, wliile he, "in tho pride of half-knowledge" 

 (his own words, for ho was one of tho manly sort), had been mis- 

 taken.— E. J. McN. (1) Distance of Betelgeux, Rigcl, and 

 Procyon not determined. (2) Have no doubt myself stars in tho 

 trapezium connected with nebula. (3) Mars now in constellation 

 Sagittarius. (4) A good bargain. (5) Only the two outermost, 1 

 think. — Dewi U. Please send order to publishers. — Diliakd. (1) 

 Sulphide of sodium is said so to act. (2) Do not think Lord 

 Raleigh said that. As a matter of fact it is not true that 

 a T chimney-pot uniformly cures smoking,— depends which 

 way wind is. — A Stident 'explains that if a plane figure is 

 subject to one condition (as that a certain curve must always 

 touch a fixed curve) it has two degrees of freedom ; when it "is 

 ■ubject to two conditiuUB, it has one degree of freedom left, and 

 can only move in a certain definite manner (2) Know very little 

 about determinants, having never wonted them. (3) My ca.ie, ns 

 yoa F.-.y. w< .-.rs :i t-kKimy asjwct, as ho would judge it. Albeit the 

 P^ ■ I cful. As knowledge advances, "the fiend of 



''■• ■ retreat.— ZcsciiAfB. I cannot think myself 



"i' irigeswhen I consider what others have done. 



1 r ■ French at seven or eight ; but would not any 



child tl.r.Kii i.Mi.rii; French children at that ago learn to talk tho 

 language r German I only learned to read by tho Hamil- 

 tonian method. Being in earnest, I learned the declensions, 

 conjugation)!, Ac, aft.ncurd*. — E. C. UooTox, E. R. IIodges. 

 Many thanks. Congratulate you on seeing transit so well. I 

 •aw nothing of it at Edinburgh, where I was. — Faciebat. 

 Yc-p, it should have U-en bisulphide of iron, the primary form 

 of which is ctibic ; it streaks dork brown. Overlooked tho error. — 

 Photo Glamjow. Do not know enough alxjut mesmerism to say. — 

 T. S. L. wants to know what is the standard catalogue of butterflies 

 anlm'.M:' W H. Jones. Believe so. Column will soon bo closed. 



J^' " '" ^ ki.— T. R. ClAPiiAM. Dawes and others, who 



'■ • -'its, have on changing focus found tho small 



'• In swarms.— D. Q. J. The letters F.R.A.S. 



' '•:.' k'uh t il:. 8 inough interest in astronomy 



'' i'ty, has been nominated by a 



•■ • members of tho society, 



'■ ' !■< fees. But there is no 



' it ions to be in any way tested. 



T ,t hj.i -ik of " tho horizontal parallax 

 '■ •" two points of observation." Tho 



'; • nly Ijody in the angle between a lino 



'•' ■"• li'.rizon, and a line to tho body 



. for a body so far off us tho 

 " 'U'k radius as arc and sun's 



more at pole than at equator; 



{ |.arily Iwcauso there is no centri- 



I'roiimity counts for something. In 

 ' vould weigh IT/Mlh Un» than a bwly 



^' ' t rfitatingj but really weighs l-lftSth 



''" ••■■ '■"•■ 1 -•'••tri being what is due to centrifugal 



tendency. (3/ Am writing a popular astronomy ; but how soon it 

 will b« 6nuhcd cannot lay.-A. B. Moli*an. The explanation is 



ingenious j but tho crescent is in tlu' lii-.st ]>laci' loo narrow, and in 

 the second, it U black coniparid witlisoliu- disc having, if of light- 

 ness of full moon— only about l-020,000tli of the liiightnoss of tho 

 sun.— A. F. OsuoRNK. Next total ecli|>so visible in Kn'glund in 2090, 

 last on May 22, 1724; baud of total iiliase just outside London on 

 the north-west.— T. A. B. filud my exiiorionoo Ciuroborates yours. 

 But I could quote multitudinous evidence. On (ho other point, I 

 have very little doubt you are right, though how many ore so nnwiso 

 it would be dilHcult to say. Possibly many. As Herbert Spencer 

 well says, tho average nmii cannot at all shako off those absurd 

 notions, oven tho exceptional man only imperfectly. I suppose I 

 must bo extra-exceptional ; for, since 1 was a lad at college, most 

 of them have boon simply nou-cxistont with mo, and tho rest 

 have gone the same way, making room for worthier thoughts. 

 Still, such nonsense is not even worth ridiculiiitr. unless unwisely 

 obtruded on notice. — W. Marshall. Qiiorica noted -, in elec- 

 trical and chemicol column may bo replied to.— A. P. Uolden. 

 Frankly, I dread tho flood of sun-spot and anti-sun spot 

 letters, articles, cuttings, &c., which the publication of your 

 letter would bring upon ns. If I note that t lie case for auroras 

 seems to mo fully made out (long since), and variation of tenipora- 

 tiu-o also, as Sir \V. Ilorschol anticipated, I have admitted nil that 

 has been proved. I think I have road very nearly all that has been 

 said for and against; and 1 must say it sooin.sto mo marvellous 

 how little eridonce will suffice with some to establish a cycle of 

 rain, storm, famines, &c. Perhaps a hundred years hence there 

 will be evidence ranging over a long enough period to exclude such 

 chance coincidences as cannot but bo observed in these matters. — 

 W.Adams. Tho secretary who "docs" my autographs is from 

 homo just now. — Dr. E. H. R. Many thanks; but literally no 

 available space. — Cor.settek. (1) Unquestionably excessive. It 

 would be nearer the mark to say that by constant lacing the ab- 

 dominal and lumbar envelopes become so relaxed and flaccid that 

 when the pressure is removed they yield seven or eight inches. (2) 

 On tho authority of all medical men, save perhaps one or two, sleep- 

 ing in tight corsets is very bad indeed for the health. (3) There 

 are doctors who have stated that at least one-third of tho ailments 

 of married women are caused by tight lacing— not by wearing 

 corsets, for whatever some caustic writers may assert, a groat 

 number of those women who say they do not lace tightly, toll tlio 

 truth ; as is shown (according to medical testimony) by the 

 shapeliness of the figure when tho corset is removed. The tight 

 lacers are known (I speak always of medical testimony) by having 

 no shapeliness at all.— W. R. The temperature of space, if space 

 is practically void of matter, would be near the absolute zero of 

 temperature, or 458° Fal.r. below zero, or 100° Fahr. below tho 

 freezing point of water, if Clerk Maxwell and Clausins are right in 

 their views about the absolute zero. — II. S. Do not know what 

 clergyman you refer to as having invented an instrument for test- 

 ing the magnifying power of a telescopic eye-piece. — W. M. Gahan. 

 Many thanks for cutting and pamphlet respecting hurricane. 



(^r iHatt)(mattcal Column* 



EASY LESSONS IN THE DIFFERENTIAL CALCULUS. 

 [Note. — These papers were commenced in No. 35, p. 83, vol. II., 

 and continued in Nos. 3G-42, 41, 46, 49, 50, 52, 54, and 57-59.] 

 No. XVI. — Integration dy Substitution. 



IT is sometimes found that an expression which cannot bo in- 

 tegrated as it stands, may bo integrated by clmiiging tho 

 variable. Tho best way of making clear the rules for doing this 

 will be by considering a simple geometrical example. 



^k 



O «- S rv M X 



Suppose wo want to determine the area A P B M a, whicli, as wc 



