183 



♦ KNOWLEDGE 



[Aug. 11, 1882. 



TiiF. riuRos AT AiEtANPiiiA. — In a letter to the Times Mr. 

 J. Kuchan Telfor. rcforriiip to the Phnrog nt Alcx!in<h-ia, con. 

 structed, accoriling to Weil, on the authority of Ijas, in 1472, 

 says the Arabian writer states that in that year u lighthouse was 

 Constructed by KaVtboT, near the old one. It communicated with 

 the city by nieau» of a dyke, and was provided with a house for 

 wor«lii|>, a mill, and a bakehouse, also a platform from which strange 

 T.-!sols conld he seen at the distance of a da/s sail, so that time 

 was afforvled for preparing the guna with which the tower was sup- 

 plied to resist their approach. The ancient lighthouse must have 

 been in eiisteno.' at soino period between the years 1425-1427, 

 because Schiltberger, who was there at that time, states that "near 

 the port of Alexandria there is a fine high tower, on which there 

 was not long ago a mirror, 4c." ; in the middle of that tower " there 

 is a temple." This account is confirmed by Makrizy (13G0-1 142) 

 who add.* that criers were seated around the mirrors to give warning 

 uimn the approach of an enemy. Abd AUatif (1161-1231) also tes- 

 tities to there being a mosque in the tower. It docs not appear by 

 the above evidence that the tower of to-day stands on the founda- 

 tions of the Pharos of Sostratns, which, however, must bo hard by, 

 and in all probability not difficult to determine. 



MoNVMEXT TO SiE E. Landseeb. — Tbo name of Sir Edwin 

 I^ndscer will no longer lie commemorated in St. Paul's Cathedral 

 merely by the granite slab over his grave in the crypt, where liis 

 remains were laid to rest near those of Sir Joshua Heynolds, Sir 

 Thomas Lawrence, Benjamin West, Fuseli, and George Dawe, the 

 historical painter. A mural tablet of marble, sculptured by Mr. 

 Woolner. has been placed about twenty paces from the grave of 

 Sir Edwin, in a bay on the south side, in wliich is John Hennie's 

 tomb, and next to that where Sir Christopher Wren was buried. 

 In the uj-per part of the monument is a medallion portrait in profile, 

 supported, as it were, by corbels on which appear copies of the heads 

 of the now famous lions in Trafalgar-square. Above the medallion is 

 a moulding enriched with fern leaves, and over this a painter's 

 palette and brushes. The lower part of the monument is a bas- 

 relief from, perhaps, one of the best known of the ])ainter's works 

 — '"The Shepherd's Chief Mourner" — which was doubtless chosen 

 as suggesting that feeling of sympathy between man and animals 

 which is characteristic of Sir Edwin Landseer's pictures. Beneath, 

 on a bracket, is the family crest, the head of an eagle holding a 

 key in the beak. The inscription, in small incised and gilded 

 letters, reads :— " Sir Edwin Landseer, U.A., son of John Landscer, 

 A.U.A. Bom March 7, 1802. Died October I, 1873. This monu- 

 ment is erected by his surviving brothers and sisters. 'He hatli 

 made everything beautiful in liis time.' " 



Bees at Koitii Kexsixgtox.— The eighth exhibition of bees and 

 their [)rodnce, liives, and bee furniture was begun on Thursday, 

 August 3rd, at the Koyal Horticultural Gardens, South Kensington, 

 by the British Beekeepers' Association. The exhibition will close 

 on Tuesday. The wet season this j-ear has not been favourable for 

 the production of honey, but, owing to the exertions of the associa- 

 tion and the local societies, the keeping of bees by cottagers is on 

 the increase. Medals, certificates, and money prizes were com- 

 I>etcd for in 45 distinct classes grouped under the headings 

 of bees, hives, supers, lioney, comb-formation, cottagers' classes, 

 foreign and colonial classes, comestibles, miscellaneous, and 

 driving competion. The display of hives was very large and inte- 

 resting. In a tent erected in the grounds the driving competition 

 was held. Prizes were given to the competitors who in the neatest, 

 quickest, and most complete manner drove out the bees from a 

 straw ifkep, and [captured and exhibited the queen bee. Neither 

 the competitor nor the judges wore veils. The driver approaches 

 the liivo and blows a little brown-paper smoke into the entrance. 

 The bees take fright, and a remarkable instinct leads them to gorge 

 themselves with honey soSieicnt for two or three days' provision 

 as a preliminary to the exodus which they forsce. In this dull 

 and lieavy state the insects arc harmless. The manipulator 

 next turns the hive upside down and places an empty hive at 

 an angle of about 4.j degrees above it. Then he drums on the 

 lower hive, l«ating it with his hands ; the bees march into the 

 upper hive, leaving the honey behind them. Tliis the honey is 

 garnered (with the exception of the stirrup-cnps which the provi- 

 dent creatures have drunk) and the bees are preserved alive. 

 Premature swarms may also be similarly made, thus saving loss of 

 time in waiting for the bees to swarm in the natural way. The 

 imjiortant thing is to see that each swarm is provided with an 

 actual or pfit«ntial queen, since she alone is cap.iblc of continuing 

 the nice. The workers are females condemned by nature and their 

 early foo<l U> a conventual life. The drones are the males, created 

 merely that one should be selected by the queen of his or another 

 hive, and should perish immediately after becoming the object of 

 her violent affcetion. The unchosen drones ore killed or driven out 

 io starve wb'Ti their brief season is past. 



^ir iWatlKmatiral Column. 



EASY LESSONS IN TUE DIFFERENTIAL CALCULUS. 



No. Vll. 



By EicnAUD A. PaocxoR. 



IN our last lesson wo established the general rules for differ- 

 entiating composite functions, and functions of functions. Wo 

 now give some examples of the npiilioation of these rules. To 

 illustrate the first rule, take the following oases ; — 



Kcquirod the differential coellioiont of a -Ho — »' with respect to a. 

 The dilTerential coofliciont of n is 0; that of x is 1, that of— »' is 

 - 2-r. Hence 



if 1/ = a ■!■ ir — ib' 



d» 

 Again put y=-(a + x-x')a'mx. 



Then the differential coefficient of (a + x-x') is (l-2,r), and tho 

 first portion of tho reqiured cocflioient is therefore 

 (l-2ai) sinm. 

 Again, tho differential coefficient of sin x is cos x. llenoo tho 

 second ])art of tho required coefficient is 



Wo add, according to our first rule, and so wo get 

 g=(l-2.) 



•(a,- 



Next, to illustrate tho second rule, though wo shall prosoutly 

 have to go back to tho first : — 



Let ■ ij={sin x)". 



Here y is a function of sin a;. So that by second rulo we treat sin x 

 as if it were the quantity with respect to whicli y is to bo dif- 

 fcreiitiateO- We know that if y were equal to a-"', its differential 

 coeflioiint would bo n .r""'. Hence in this case wo have for tho 

 first factor of our coefficient n (sin ir)"~'. But tho rulo tells us wo 

 are to multijily this by tho differential coefficient of sin o), that is by 

 cos X. Hence we have finally 



^ = n(sinx)'-cosx. 

 dx 

 Take another case. 



Let i/ = (a»-fa;=)t. 



Here y is a function of (a' + x'). Hence by the second rulo wo 

 treat (o'-t-a;') as if it wero tho quantity with respect to which y in 

 to bo differentiated. If y were equal to rt* wo know that its dif- 



We are to multiply this 

 -that is by 2 ir. Therefore 



of the required coefficient is — r-= irr-,- 



' 2 {a? + x^)i 



by the differential coefficient of (a' + a^),- 

 we have finally 



(?;/ 2X i 



Yet one more case of the second rule. 



We know that if i/ wero equal to - or x"' its diffi.Tcntial coefficient 

 would bo -x~"; or ---. Hence the first factor of tlio required 



I 



coefficient is 



We must multiply this by tho differential 



(sin x)' 

 coefficient of sin x, that is by cos x. Thus wo get finally : 



d;/ _ cos » _^ _ - _. (,n.„(.J r 



dx (sin ic)' 

 This is one of tho results already obtained. But obsorve specially 

 that the differential coefficient of tho recij)rocal of any quantity may 

 be shown in precisely the same way to bo the reciprocal squared 

 multiplied by the differential coefficient of tho quantity taken 

 negatively. For example : — 



If y ='-J-. 



dx {a' + x')' (a'-t-x'j^ 



And now finally (so far as the present lesson is concerned) lot us 



take a case in which both of our rules arc ajjplicd, but more 



directly dealt with under sub-rule C, for the caso of a function 



I 



