1G6 



KNOWLEDGE • 



[Dec. 23, 1881. 



contact with the outer world, for tho work before it? But wliilHt 

 the lot of most women (without beiiiff doomeJ to " suckle fouls and 

 clironiclc smnll-hccr ") is yet to fill, ns intelligently and happily as 

 may be, tho domestic posts of daughter, sister, wife, and motlicr, 

 would it not be unfair to call upon them to exhibit qualities for 

 which they would have no exercise, and which, if ever needed, 

 come with the need? The "Jack Sprat" story of our nursery 

 days wouUi be falsified if men and women were made exactly alike, 

 and I fear the result would sometimes be that the domestic platter 

 would not bo " licked clean." I may bo wrong, being 



Only a Woman. 



P.S. Let me add one word of grutcfid thanks for your paper. 

 May it have tho .success it deserves. 



Kdinburgh, Dec. 9, 1881. 



ANOTUER TRISECTION' OF AN ANGLE. 

 [142] — I send you another method of trisecting an angle, more 

 suitable for practical purposes. Of course it rccpiircs the ordinary 

 mechanical contrivance, but as the point P is iirbitrary, and CD is 

 double BP, these measures can be permanently marked on tho 

 scale. To trisect any anirle :- - .IRr is the riTitrlo. 'niki^ niiv point 



I' in Mi, draw i'Jf parallel and I'N perpendicular to BC ; from B 



draw BD so that VD=2.BP; bisect I'BD. The lines BD and BE 



trisect the angle. The proof I leave to the ingenuity of your 



i-eadcrs. It is very simple. — Voms, &c., ,S. B. 



15, Bessborough-street, St. George's-sq., S.W. 



[This is the method invented by Pappus, of Alexandria. From it 

 we can easily see that the hj-perbola is a trisectrii. — Ed.] 



VARIABILITY OF PENDULUM. 



[113] — There is a misapprehension here founded on want ot 

 precision in ideas. The writer points out " a difference of velocity," 

 but omits to specify to what point he refers as the standard. 

 Apparently, however, the centre of the sun is intended, for which 

 his statement is approximately correct ; but tho motions of the 

 pendulum are controlled by the mass of the earth, generally 

 reckoned as a force acting from its centre, and with reference to 

 this latter point, no such inequality of velocity exists ; so there is no 

 ground for anticipation of any ditu-nal variation dependent on this 

 (supposed) cause. Couito. 



ANTIQUITY OP THE PYRAMID.S. 



[Ii4] — It is impossible in the spac-e which could be allowed in 

 Knowleugk to give adequate reasons for believing some of the 

 l>yramid8 to be 6,000 years old. If " Actinolite " (querj- 72, p. 122) 

 wishes to know the best authorities on tho subject, he will fiud 

 Rrugsch's " History from the Monuments," Uawlinsnn's or Erasmus 

 Wilson's " Egypt," and a work published by Macmillan, entitled 

 " A Rido in Egypt," by Mr. Loftie, give him ample information. 



If Egyptologists are correct in assigning tho Pyramid of steps at 

 Siikkara (which, by-thc-way, differs from all others in not following 

 the cardinal points of tho compass) to Vauepbes of the first dynasty, 

 .Sir J. Lubbock would probably be within the mark. The Pvramid 

 of Scnerferoo, eighth king of the third dynasty, is at Mavdoum, 

 and may well be as old as ti.OOO years. For the date of Jlenes is 

 fixed as 5702 ii.r. by Ba'ockh, 5,000 ii.c. by Prof. Owen, Marriette, 

 and Manetho, 1-,155 by Brugsch, for which he gives excellent reasons, 

 ■1,500 B.C. by Maspero, 1,000 n.c. by Chabas, and 3,892 B.C. by 

 Lepsius. English authorities prefer a shorter chronology, Mr. 

 Stuart Poole even favouring 2,717 n.c. 



It may lie said that all tho occumnlating digcovcrics go to prove, 

 with sliglit exceptions, the validity of Manetho's list and dates. 

 For instance, one of bis supposed mythical assertions with regard 

 to a King Apappus, that he was a giant, and reigned one hundred 

 years, lias recently been confirmed by a monument now at Boulaq, 

 mentioning tho one hundredth year of his reign, and bis hieroglyphic 

 name Papi means a giant. This longority is 8urpa.ssed by tliat of 

 Assa and )iis son Ptah-hotep of the fifteenth dynasty, who, according 

 to tho Prisse papyrus, must have lived over 130 and 110 years 

 respectively. See " Smith's Bible Dictionary," I., 322, where these 

 facts are used aa arguments in favour of the long lives of some of 

 the patriarchs. 



It is important to recollect that if the monuments are held to 

 confirm tho old supposed chronology of about 4,000 years from the 

 creation to the time of Christ, they witness in favour of the plurality 

 of the humau race, because they show (|uite as great a divergence 

 between tho negro, Egyptian, and Asiatic ty])e8 on the earliest 

 monuments as at the prefent time, and so there could not possibly 

 have been a sufiicient period for such a differentiation from the 

 progeny of a single pair. 



A Membee of the Society of Biblical ABcn.EOLOGV. 



SOME SUGGESTIONS RESPECTING " KNOWLEDGE." 

 [115] — 1. 1 think it would be a great advantage to many of your 

 readers if in your notices of books (which I hope to see soon) you 

 stated the price as well as the publisher's name and address. 



2. Sale Column. — Do not you think that a sale and exchange 

 column (such as in the Enylish Mechanic) would be a good addition 

 to K.NuWLEDGE? Through it Subscribers could exchange and sell 

 scientific works, telescopes, aquaria, &c. 



3. Collections. — Shall you have papers on making collections ot 

 all kinds of natural objects, such as a herbarium, butterfly collec- 

 tions, geological, bird and fish stafiBng, skeletonising, insect taxi- 

 dermy, &c. ?— [Freshwater aquaria. — Ed.] 



4. I hope you Avill foretell all natural phenomerm, such as 

 eclipses, meteoric showers, &c. (as far as you are able), asd how 

 best to be seen, by naked eye or telescope. E. R. C. 



THE THREE-SQUARE PUZZLE. 



[146] — Mr. Langley's note (Xo. 97) reminds me of an old puzzle 

 which was set to me in Germany a good deal more than forty years 

 ago. It is, in fact, a variant of his, and shows how his five pieces 

 are obtained. It also always seemed to me to bo the best proof of 

 the celebrated 47th proposition of Euclid's first book. 



Take any oVilong piece of paper and fold down two csmers, as 

 along AB, BC in the figure ; then, by cutting along AD and CK, 

 you obtain two adjacent squares, AGBD and KBHC. Now, the 

 puzzle is by one cut with a pair of scissors to cut these two squares 

 into three pieces which will themselves foi-m a square. I>et those 

 wlio arc foiiil of puzzles attempt it mthout reading what follows. 



Solution. — Fold the paper so that the point C lies on the point X. 

 Then the fold will be along the line EF, giving tho poiut E, where, 

 of course, EH = GB. Cut with the scissors through both of tho 

 folded sides fi^om A to E, and C to E, by one cut. Then you have 

 the two triangles AGE, CUE, and the shapeless remainder. This 

 done, I may leave any child to fit them into a squai"e, and any young 

 geometer to prove that that square must be that on the hj-po- 

 tenuse of a right-angled triangle of which the sides are also sides 

 of the two S(iuares. Observe, that if you also cut along BD, you 

 get Mr. Stanley's five pieces. — Yours, &e., Alexander J. Ellis. 



