504 



• KNOWLEDGE • 



[Apbil 7, 1882. 



Tho thiith-lHinra worn vorv ulroriKly rid^foil, iiuliculing (rrrnt ninii- 

 riiUr |H>wi'r; mill tlii'm wi<rt> aUn fouiiil . a<iiuciutcd with it 

 Iho can- Iwnr, li«<T, liyii-iin, mid wocilly rliinnccro^. 2. Tlie> 

 KiiKi* nkiill wiw fmiinl iii'iir I.ii'-Ki'. Dr. SiliiiiiTliiiK fi^'iirrd it 

 ill 111* w.irk, liiit wliilnl cibwniiiK tliiit it wiui too impiTfiTt to 

 ulTurd niir dcliTiiiiiintinii nf fiiciiil miKlc. he nMiiiiK'd thnt it I>oIiiiik<mI 

 (II mi jiid'iviilunl iif low iiit«lliirliiiil ili'Vi'lii|iim'iit. Mr. Bunli Hnyii it 

 niiiflit l>i> nmti-lii-d by imlividimlB i)f Kiiropcnii rnce, nnd in tliiii 

 iipiniuii iiiiint )(i'<i|iiKi»tii nnd niintiiiniiitii nKToo. Thia akiill in of 

 PJvintiirciiii nm\ lliixlfV unyii tliiit " llic cnpnclty €>f thp iiitiTior 

 • if thin frntfiiu'iilnry nkiili lm» not been imocrtuincd (" Miin's I'l.-i'i' 

 ill Nnliirr," pn^u 12H). Bntli Nonndurtliiil ami Enffis ekullH bi'InnK 

 »« till- ririntiK-iMw iieriod. The fornuT in ciTtainly the hiwost type 

 of huniiin iikull kniinn. 3. Mr. Kinko'n " postuhit'c " (K.No»l.KnoK, 

 pnjfn UiM, So. 11) iiiniply n<cnpiliilntcii an underlyinR assumption 

 <>{ till' whole sint.'iiieiit of the ruse for evolution. It is a needful 

 IHiatuliite for the |K'rwiii who is i)fiiorant of, or opposed to, evolu- 

 tion. I'or one like Mr. llomson, wlio admits tho truth of evolution, 

 it is simply nn additional proposition. 



EI.ECTUICAL. 

 Wm. Pleulnc. Good cxaminntion certificates have some little 

 weight with electrical en^fineerinfj firms when seloeting their 

 rmiiloiit'n, but the industry is very younp, and practical knowledge 

 d«, therefore, generally looked for. Try the examinations of the 

 City and Guilds Technical Institute, Gresham College, E.G. The 

 secretary will send particulars on speedy application. You may 

 study with advantage Spnigue's "Electricity," Galley's "Tele- 

 graphy" (the latest edition— seventh), and Unjuhart's "Electric 

 Light." — G. U. U.iRKi.i. It is not so unusual as you imagine 

 to sec a magnetic needle in which both ends are of the same 

 polarity. If you carrj- your eiperiment a little further, you 

 will find tho other or opposite polo in the middle of the needle, 

 there being in this case two neutral zones. The centre pole will, of 

 course, be equal in strength to the sum of the two end poles. — 

 JiMEs Gbi'ndv. 1. Tho manganic di-oxide and carbon in tho Le- 

 clanche cell should bo about equal in quantity. Govering in the 

 |H«rous pot with pitch or marine glue keeps the contents in 

 position, but be careful to leave a vent-hole for the escape 

 of any gases that may be evolved in the cell. Use crystal- 

 lised sal ammoniac and water for tho outer cell. 2. You can 

 only determine the value of the current obtained by measurement 

 ILarc yon the means of doing this 'f 3. What is the specimen of 

 wire yon enclosed ? Is it aluminium ? It is too dirty-looking for 

 platinum, nor does it test like it. The resistance of about one 

 foot of it is only O'O'.'G of an Ohm. One hundred Leclanche 

 •cells failed to raise a couple of inches to redness, bat 140 cells 

 make 3 feet red hot. l. The electro-motive force of a Leclanche 

 ■cell is about I'G Volts, the Grove being 1-8. — W. G. Fixcii. 

 Electrical tricycles are not the only things missing in the 

 Crystal Palace Exhibition. To work a tricycle you would 

 reijuiro a motor, with a batten,-, or its equivalent, to work it. I 

 know of none before the public, but believe ono is soon to be offered 

 by a Manchester hou.so. — A. E. Smith. A series of articles on 

 •dynamo-electric machines is now appearing in this journal. lam not 

 quite sure what you require. If you do not see it, write again. — 

 S. B. Galvanic batteries of the Danicll, Leclanche, and bichro- 

 mate typos arc used by the Postal Telegraph Department. The 

 electric light couW be produced by them, but neither efficiently nor 

 economically. £5 or £C spent in Bunsen or Grove cells woiild yield 

 an electric light for three hours or so. — H. A. B. " Lightning pro- 

 tector " is a better name than "lightninfi; conductor." Its chief 

 »vork ia to neulraliae the electricity of the overhanging cloud by 

 discharging into it an equal quantity of tho opposite kind, which 

 is drawn or attracted from the earth by tho electricity in the 

 cloud. Should it happen that the protector cannot discharge 

 •piickly enough, then tho cloud-charge strikes towards the earth ; 

 and as tho protector is tho noiirest object, nnd offers the easiest 

 means of passage, thi.' electricity from tho cloud passes through 

 the protector to tho earth. Consequently, the more good 

 protectors you have, tho safer will your house be, as each 

 ono added is another possible channel of escape. — J. R. Wilson. 

 Read preceding answer. The proper hnight of the lightning 

 protector will do|H<nd on tho area it is intended to protect. 

 Cop|K>r, in the band or rope form, with platinum points, is the best 

 material. As, however, there is cunsidornble diversity of opinion 

 on tho quostiun of moa.suremont, Ac, the subject will be dealt with 

 in an article in this journal a week or two hence, when it is hoped 

 you will find all you require.— C. 11. W. Dynamo-electric machines 

 are of so recent n birth that it is hardly fair to hwk just yet for any 

 great flood of literature upon the subject. Efforts will, however, be 

 Hindo to supply shortly the information required by those who aro 

 Miiiioua to make machines for them^ielves. 



Onv i¥latl)fniatiral Column. 



PROBABILITIES. 



Tu the two examples in our lost the following may be added : — 



3. How many trialt iri(/i a full pack jive an ef»n ehanee of eullinj^ 

 nti'j -lircn card {of a giren luil) ? 



The chance of failing to cut the given cani in a aingle trial is — , ■ 



('il \' J 



'-_ J , and so on. If n be the number of trials, which i 



will give an even chance, wo have — 



&-i-m-'- 



Uenco, taking logarithms — 



71 (log. 52 - log. 51) = log. 2, 

 or 81331n - 3010300 



whence n = 



3010300 



= 35-; 



81331 



whence 3G trials will give slightly more than an even chance of 

 drawing the named card. 



4. In how viany triala will there be an even cliance that dealer 

 at U'liist jcill have all the trumpn. 



The number of possible hands which dealer can have is the 



number of combinations of 12 cards which can be made out of 51, 



and this number it will be found on trial is 158,753,300,900. Hence 



the chance that he will not have all the trumps. 



^ 158,753,38i),8il!) 



158,753,389iy00 



and to give the number of trials, n, in which there will be an even 

 chance that dealer will have all the trumps, we have the equation 

 158,753.380.899 \n 

 158,753,389,900,/ ~^ 



Vl5 



Whence, approximately, ( — '^ | 

 V 15,876/ 



= i 



And taking logarithms. 



(log. 15,876 - log. 15,875) = log 



10,0jli,0jo 

 or 273,555n = 30,103,000,000,000,000 

 [To get the difference 273,555 corresponding to logarithms to ten 

 places of decimals subtract logarithm of 15.860 from logarithm of 

 15,890, and divide the difference by 30. This gives near approxi- 

 mation to the difference between logarithm of 15,876 and logarithm 

 of 15,865. But to get nearer still, do the same with logarithms of 

 15,861 and 15,891 ; add the results thus obtained, which are 

 respectively 27,357 and 27,353, and halve — giving 273,555.] 

 30. 1 03,000,000.000 .000 



or n = '-ij too =110,400,000,000 



This, then, in round numbers, would be the required number of 

 trials to give an even chance of a deal in which all the trumps 

 would be in ono hand. 



Problem 5. — H/ipii the n umber of possible events, all equally likely, 

 is venj great, to determine what ratio the number of trials necessary 

 to give nn equal chance of any given event bears to the total number 

 of possible events. 



Let the total number of events be X, then the chance that any 



A'- 1 



given event will not occur in a single trial is — rz— j and if n be the 



number of events necessary to give an equal chance of the occur- 

 rence of that event, we have, as in the previous case. 



(j^)'"- 



nJlogiY-log.(.Y-l) I =Iog 



.^ f 1 1 



2iiu < + 



t 2.Y-1 3(2iY-l)' 



+ &C. 



\^ 



3010300, where /i iR 



tho iiiodiiUis of the common system of logarithms, or the reciprocal 

 of tho Nepcrian logarithm of 10 ; whence, when A' is very great ao 



that . 



2.Y-1 JV 



•3010300 3010300 



= "^"-f^ = 0-6931472 ( = Iog.,2) 



N fi 4342945 



If wo apply this rule to the previous c.ise we get a value very 

 cl )se indeed to that already obtained in another way. 



