78 



KNOWLEDGE ♦ 



[Aug. 3, 1883. 



of the time." The omission of the words "too conspicuously" 

 completely alters the meaning of the sentence. E. M. Kxng. 



[We gladly give Mrs. King's letter insertion. The omission of 

 the words was due to a printer's error. — K. P.] 



OLDEST HISTORICAL TREE. 

 [891] — In answer to " Cosmopolitan," the Bodhi tree at Aiiarad- 

 hapnree, Ceylon, is the oldest historical tree in the world — not the 

 oldest tree. That at Buddh Gaya, near Gaya, from which it was 

 taken, was destroyed, and two or tliree of its successors also de- 

 stroyed. The iirst destruction took place under the orders of 

 Asoka's Queen. The present tree is quite young. I send you here- 

 with a printed account of my visit to it two years ago. 



K. S. Macdonald. 



LETTERS RECEIVED, AND SHORT ANSWERS. 



51. DoiBLEDAY. Evil all the time, is there not ? — R. Thomsox. 

 It would be difficult to say what the capsizing influence of the 

 current would be on a ship launched as the Daphne was. — S. J. 

 Potter. Foretelling destiny by aid of planets sheer nonsense now- 

 a-days, but a not unreasonable notion in old times ; the most re- 

 spectable of the old superstitions. — R. F. Keer. If I could define 

 that word, I should know something indeed. "Can'st thou by 

 searching," &c., they said in old times ; so must all say, throughout 

 all time. — E. B. would be obliged if " Pedestrieune," through Know- 

 ledge, would say where the pattern she speaks of, with instructions 

 for making up, can be obtained. — Z. I should say, and so says the 

 writer of the articles in question, a manifest swindle. You will 

 find no chemist to make up the prescription sent you, so must 

 send to advertiser, who charges an exorbitant sum, for a draught 

 possibly worthless, but most probably exceedingly harmful. — 

 W. Woods Smyth. Does Mr. Herbert Spencer's rule for moral 

 action enjoin us to seek our own happiness supremely ? You 

 astound me ! I thought there was precisely that principle of equi- 

 libration in his system of ethics which there is in his system of 

 philosophy generally. Really he seems to say so. But perhaps he 

 does not know his own meaning. Let us wait to see what Mr. 

 Foster makes of it. Only, frankly, if Mr. Foster shotild work out 

 your result, or anything so remote from Mr. Spencer's own 

 teaching, the editor wiU interfere in a very summary manner with 

 his friend Mr. Poster's series of papers. This is not likely, though. 

 — Tbos. Westlake. Out of your own mouth (or from your own 

 pen) you shall be judged. " When wiU men see," you ask, that 

 there are two revelations of God, one in his works, and the 

 other in his Word ? We cannot perhaps always see at once how 

 they harmonise. But we answer they do, and we shall by-and-by 

 know how." Yet you are sorry that a series of articles should 

 appear in these pages, the object of which is in the main, as I 

 understand Mr. Foster's purpose, to show that practically the same 

 moral laws result from natural processes affecting the condition and 

 progress of God's work — man — which have been enunciated in 

 those works which you regard as His word. Your contention is 

 unreasonable. — E. C. H. I had the pleasure of conversing with 

 several representative members of the Worthing audience, and 

 think you are mistaken. Friends who were in the audience think 

 so too. Though of course there were many there of the class you 

 mention. — G. S. Question considered. — Leonard Brown. Shelley 

 there obviously attacks the argument from design, but his sugges- 

 tion of the line of reasoning followed later by Mr. Herbert Spencer 

 (the real originator of the environment doctrine) is too vague to be 

 regarded as an anticipation. — J. Russell, B.A. Question does 

 not admit of a solution as stated. — Ixquiker. Two or three months 

 ago the problem of 21 school-girls was solved in a systematic 

 way ; easily extended to the case of 15. The problem is not in 

 any case a simple one. — E. B.^rtox. Certainly hope to give a 

 course of six evening lectures in Manchester before I leave Eng- 

 land. — W. H. B. Ranixe(?). I believe the flat earth men have no 

 knowledge of what has been done in the way of Antarctic ex- 

 ploration. — C. Thosipsox. An instrument for assisting the hearing 

 was invented by a Cliicagoan a few years ago ; it was a tautened 

 surface of card or tin, japanned, and held by a handle with the 

 middle of the outer edge between the teeth. As nearly as I can 

 remember, it was about as large as a medium-sized fan. Possibly 

 some reader may be able to give an account of it. — E. W. Tawom (?) . 

 Thanks ; but the conjuring trick rather complex. — H. C. JoxEs. 

 In that sense I am already a member of your " Society for 

 correcting, detecting, and where necessary exposing slander." 

 Much obliged for youi- very kind remarks about my South- 

 ampton lectures, and your report of the kindly acceptance 

 they met ivith from your friends. We lecturers are sup- 

 posed to be so possessed with the sense of our constant 

 rightness, and the eternal fitness of all we say and do, that we 



onght not to hear of any kindly things said of us, — whereas as a 

 matter of fact we are a race of " nervous, shy, low-spoken men" 

 like the Coxswain of the " Mantelpiece," and " not to be treated nn- 

 benignly " as Tennyson puts it. — C. J. R. Richards. Those who 

 often tell you that geology disproves evolution because in the 

 lowest fossiliferous rocks animals of a higher organisation have 

 been found than in the upper rocks, should often study a little 

 geology. The statement is untrue in every sense except thus far 

 that just as at the present time there co-exist higher and lower 

 organisations, so has it been in past times ; and some of the organi- 

 sations of an older epoch are necessarily higher than some of the 

 organisations of a later one, even of the latest of all, the present. — 

 A Student. Quite unable to answer such questions ; it would 

 afford a bad precedent, and moreover lead to a great deal of annoy- 

 ance. — Hugh Clements. " Great earth dominating planets." Great 

 earth dominating fiddlesticks ! — J. W. C. " Say about one inch 

 apart," — all right, I say that : but I do not say what the power of 

 your telescope is. Seriously, one such question answered here 

 would bring a hundred ; each of these many more, and Knowledge 

 would be killed by kindness — its editor's. — H. T. Pekky. Thanks : 

 but matter hardly important enough to be re-opened. — J. Greeves 

 Fisbee. Yes : but your account of the puzzle does not tell us what 

 would happen if some other number than " one " were thought of. — 

 S. M. B. It should be tolerably obvious that Mr. Ledger and I 

 both made the same blunder, speaking of the day as shortening 

 instead of lengthening, though elsewhere we had each carefully 

 shown that it is lengthening, and how, and why. 



^^r iHatftcmatical Column* 



GEOMETRICAL PROBLEMS. 



By Rich.abd A. Proctok. 



PART X. 



Let us next try a problem which is the converse of Example 5. 



Ex. 13. — To determine the greatest of all the triangles which can be 



constructed upon a given base and with a given perimeter. 



Fig. 21. 



Let A B, Fig. 21, be the given base, C the sum of the remaining 

 two sides. 



Now, with a knowledge of the property established in Ex. 5, it is 

 of course very easy to see what is the solution of our problem. But 

 we shall assume that the student is deahng with the problem in- 

 dependently. With centre A and radius equal to C describe the 

 arc D E F, and draw radii A D, A E, and A F. Then if from B we 

 draw lines B G, B H, B K in such a way that B G is equal to G D, 

 B H to H E, and B K to K F, it is obvious that each of the triangles 

 AGB, AHB, AKB has the required perimeter. Now it is an 

 obvious consideration that if B G is equal to G D the angle G B D is 

 equal to the angle G D B (we here draw in B D) and, therefore, 

 that in order to draw B G so as to be equal to G D, we have only to 

 make the angle DBG equal to the angle G D B. So that having a 

 construction for determining any number of triangles, it is pre- 

 sumable that we shall find materials for determining the triangle 

 of maximum area. But first let us see if anything is suggested by 

 an examination of the figure. We see first that the triangle 

 gradually increases as the angle at A increases. But there is clearly 

 a limit to this increase. For it is obvious that we might have 

 taken B as the centre of a circle with radius C, and thus have 

 I shown that the triangle increases as the angle at B increases. We 



