Aug. i, 1S82.] 



KNOWLEDGE 



171 



(Jl^ur ^Jnrntiov Coliinin. 



A CoBRESPONBENT thinks an occasional Tarailox Column might 

 afford instruction as well as amnscment. I think so too. But juat 

 now I think more of the evidence such a column might afford, that, 

 ill not admitting certain letters and theories into Knowledge, I 

 have been guided by the honest belief that they are not strictly 

 scientific. Now here is a letter which, oddly enough, was opened 

 next after the one asking for paradoxes. What can one do with 

 such commnnications ? 



The P.D. TiiEor.y. 



EDITOR, I flatter myself that the P.D. Tlicory has a good hold, 

 but, mistakes are so easily made ; If the Theory of the P.D. 

 Sir has any weight in it, lot it go ahead, 1 am sure it will find ils 

 road through all other theoi-ys, as it is composed from a natural 

 idea, taken nature to have only one course, path or way, nature 

 cannot go the wrong road without a change takes place, which it 

 cannot change its-self as there is only the one way, and that way 

 is its-self, it has the whole within its-self, nothing can change with- 

 out been mixed, nature is pure, if it wore to change by been mixed, 

 it would not be pure, nor would it be natiii-al — nor would there be 

 any nature ; Then what would we have, (N'othing) oh no, time says 

 there has always being something or else the light of our sun could 

 never be ever-lasting and pure ; AVhich denotes all things in one 

 class to be of one class or quality ; sho«-n. that all planets are of one 

 class, and all stars are of one class, also all of one class must move 

 round one way, there is no other way in nattire ; the same with 

 comets and meteor's, every thing in nature is self-acting, the snn- 

 l)eams upon our earth until it rises a vapour and spreads it like a 

 sheet which acts as a safety-valve or else our gi-een carpet would 

 soon be dTsmantled, we would not have any light if the sun did not 

 rise the vapour every day, as light cannot light without something 

 to light upon, nor can we have heat without the hght, or else every 

 thing would be cold, dark and Ufeless. 



Sis, — I cannot see in any way the P.D. Theory has taken harm 

 by the new photo of A. C. Ranyard comet shown in Kxo. — July 1-t 

 — 1882 As we have only the one front view of comet, the tail 

 might have a very short or quick radius, but according to radius so 

 will the distance be from the centre, as gravitation has its radius or 

 l;nv worked from the centre ; judging from its tail, it must be a full 

 grown comet, such ns seen in gone by times when they looked 

 beautiful, old comets that appeared in olden times looked like a sun 

 without any tail 



.Sir, — I would like to see Mr. R. A. Proctor, Try this system (on) 

 one twelve months. Or give me the address of one a American 

 :i-tronomer. a go ahead party. J. Ml'kkav. 



^rt'cnrr ani) art ^Iros'sip. 



I'KOFES.^oK Looms suaos that the h.aviuf.t rainfall is met with in 

 ilie rain-belt which surrounds nearly the whole globe lying between 

 the north-east and the south-east "trade winds. Mr."W. J. Black, 

 having been engaged in collecting reconls of rainfall at sea for 

 i.onie time back, gives an estimate of the rates per annum for this 

 lain-belt. That for the Atlantic (leoan is calculated at 133-37 in. 

 ()or annum, that fcr the Indian Ocean at KO'Soin. per annum, that 

 lor the Austral-Chinese seas at lOT'lMi in. ; but none has yet been 

 made out for the Pacific Ocean, owing to absence of observation 

 altogeilierfrom that quarter. 



MiMXO Statistics.- The Mines Ins.rctor for North Staffordshire, 

 f'heshire, and Shropshire, Mr. Thorn is Wynne, reports tl^at the 

 number of persons employed in the various mines under his juris- 

 • liction during bst jear'was 2t,4ii;i ajrainst 2-',S52 in l^^SO; the 

 ipiantity of minerals raised w.vs 8,1) 1 1.382 tons against 7,57<>,1t)0 

 ii>ns; the number of persons cmpliyed to raeh fatal accident was 

 ."•S3 agninst 170: the number to earlilife lost was ol8 against 206; 

 the tons of mineral raised for each fatal accident were 205,818 

 iigainst I57,8i2 ; tons to each life lost, 112.201 against 08,205. The 

 number of mines was 210 against 3-lo, and the non-fatal accidents 

 were 313 against 321. 



Tree Bukial in New Zkalaxd.-- The recent fall of an enormous 

 puketei tree near Opotiki, New Zealand, disclosed the fact that tie 

 Inilliiw interior from the roi'ts to the lii^t lurk, about fc rty-live feet 

 li-om the ground, had been lilled witli huinaii bodies. A confused 

 li.-iip of skeletons burst out of the butt of the tree when it fell. .V 

 I'lrnl paper says : — " A more extraordinary sight than this monarch 

 of the forest lying ]>ronc and diseharging a perfect hcealoinb of 



human skeletons can scarcely be conceived. Some are nearly 

 perfect, while others are mixed up in a chaotic mass of heads, 

 hands, feet, and arms, indiscrimiDatcly. All the Maoris here seem 

 to have been quite unaware of this natural chamel house, and 

 declare that it must have been filled long before their or their 

 fathers' time. Indeed, the appearance of the tree fully justified the 

 supposition that it must have been some hundreds of years since 

 this novel family vault was filled witli its ghastly occupants." 



Mr. BorcicAn.T on .\tTiNG. — On the stage of the Lyceum 

 Theatre, on Wednesday (20th inst.), Mr. IJoucicuult delivered to a 

 large audience of actors and others interested in the drama a lec- 

 ture on the "Art of Acting; Its Rules and Principles." The 

 lecturer's object was to show that acting might usefully be taught 

 like paintirgand other arts. With this view he dealt with his 

 subject under the sevenil heads of articulation, gesture, posture, 

 and study of character, each of which he illustrated from his own 

 experience of the stage. As regarded gesture and posture, in par- 

 ticular, he showed that the true principles of the art existed merely 

 as a tradition, and had to be picked up by the conscientious actor as 

 best he could. It was not enough to Iiehave on the stage as one 

 would do in real life, as the lecturer proved by the simple act of 

 jiicking up his hat from the table to walk out. Tho actor had to 

 remember that his every action was presented as in the frame of a 

 picture, and that it had" to be studied with reference to the effect it 

 woidd produce upon the house. Thcart of listening, and of continuing 

 to sustain a character, even when he had nothing to say, was therefore 

 an important yiart of the actor's art, though a part, unfortunately, 

 much neglected. Under the head of posture, the lecturer insisted 

 upon the necessity of cultivating the "lost art of walking" — an 

 art now possessed only by uncivilised people, whose ankles had free 

 play, and who were in the habit of carrj-ing weights upon their 

 heads. Q'he study of character, he showed, ought to bo " fr«m 

 within" and not " from without." In other word?, the character 

 ought to be drawn from tho nude, and the costume fitted to it 

 afterwards. It was also desirable, whenever psssible, to study a 

 character from life, as Charles Mathews and Farren did for their 

 parts of Dazzle and Sir Harcourt Courtly in " London Assurance." 

 On all the points the lecturer contended that a course of instruc- 

 tion, such as was followed at the Conservatoire, would be beneficial 

 to those who desired to adopt the stage as a profession. The 

 lecture, interspersed as it was with much genial anecdote and 

 practical illustration, was both entertaining and instructive, and at 

 its close Mr. Boucicault received the cordial thanks of the house. 



^ir iSatDfinatical Column, 



EASY LESSONS IN THE DIFFERENTIAL CALCULCS. 



No. Yl. 



By Ritii.\SD A. Pro(tob. 



WE have now to establish rules for dealing with compcsite 

 functions, and functions of functions. 

 First let us fake composite functions!— viz. (i.), the sums and 

 differences of functions, (ii.) the products of functions, (iii.) func- 

 tions divided by functions. 



I. Let i( = r-! 11-'; + :, Ac, where r, v. y, :. Ac, are all func- 

 tions of J ; and when x is altered into (x + A.'), let « bo altered into 

 (,(+ All), ''into (c+ /^v), "into (hm- £,,<). &c. Then 



„+ A»-(c+Ar) + ('r+ Aif)-(y +&:/)+(:* At) + *<• 

 II.Miee, subtracting the former equation fiom the latter 

 Au= Ar f Air- Ai. + A: + Ac. 

 and .lividing both sides by A r, we have 



Now, suppose Ax to become indefinitely smiill, sv) that _-- 



A'!' , A'l , ^J. , Ac, become the differ, mini cvllioienta of 



Ai- Ax At 



y, ;. Ac, with respect to r. Then we have 



rfii ir dtr _dii dz ^_ / ^. 



Ji'di Ifr'Tr Jx "■ 

 II. I.el M - •! : ,- V. :. as iK-forc lioiiig fTrcli.m.s i>f :, a 



