82 



♦ KNOWLEDGE 



[June 30, 1882 



anstorrsf to CorifSponijnUg. 



((f KsoyiLiBai, Uu 

 information 



AU t*mmtMctH»mM ftr tU Bdilor rtfMirimf tarif 



>■ T itfoTt Ikt SattrJiij prtrrdf} Ike nrrnt iuii 



<••/ nmlat>a» ^ K»ir» rtmftU mi to go to frtu tarl) 



rrs to Co»l«sro!ir»!iTS.— 1. A'o quntionM a»J-i»j /or tcintijl. 



' autvfTtJ tkrcmgk tktfott, i. lftter$ irnt to the Editor fore 



t be forw,rrJe4 ; nor eon the namet or addreuee ^f eorreepondeuti be given in 



r to fnctite tmqninet. 3. CorreepondentM ekomld ttrite on one tide onlg of 



Ja>. Ufjis. On re-reading, yonr lelter seemed not to contain tlie 

 direct positive evidence necessary to make such cases scientifically 

 useful.— \V. H. Bi-TcnART. Mr. W. Maltieu Williams has not yet 

 published his promised work on " Comets and Xebuhv." — R. 

 Shewaed. I fear it is hardly in favour of your theory of solar 

 energy that it is "distinct and separate from any known." I do 

 not rvmember any true theory of which this could be said. At 

 present, however, my chief difficulty is that the theory could not bo 

 condensed into less than ten pages of Knowlkdge. Perhaps, if you 

 published it elsewhere, we might manage to give the essence of it 

 in less space. — E. D. G. We agree with you that Col. Ross's defini- 

 tion of analogy is incorrect. As in mathematics, " Analogy or pro- 

 portion is the similitude of ratios," so in general anology signifies the 

 similitude of relations, not resemblance between things. — A. McLean. 

 Many thanks. Your suggestions are all eicelleut. I proposed such 

 a publication to one of the principal publishers of Victoria ; but his 

 idea wus that it would hardly pay. If readers of Knowledge would 

 not object to a series of maps doing for the southern hemisphere 

 what those now publishing do for the northern, that would bo a 

 convenient way of producing the work. I think many, though 

 living in the northern hemisphere, might like well to know the 

 aspect of the constellations in the southern skies. — C. L. 13. Let 

 A B C be any triangle ; P, Q, R, the centres of equilateral triangles 

 on A B. B C, A C. Through A, draw a straight lino parallel to P R, 

 meeting the circles circumscribing the equilateral triangles on A B, 

 A C, in <• and b respectively. Thus it is obvious that b B and cC 

 produced must meet on the circle circumscribing the equilateral 

 triangle on B C (since the angles at 6 and <■ are each one-third of 

 two right angles). The triangle a b c is equiangular, and, there- 

 fore, equilateral. But b c being the greatest chord which can 

 be drawn through A to the circles b, <-, it follows that 6 o 

 and c a are also maximum chords. (For if longer chords could be 

 drawn through B and C, their extremities wonld give an equilateral 

 triangle circumscribing ABC, greater than ab e, or be would not be 

 a maximum chord.) Hence b a and c a must be parallel to P Q and 

 RQ. (For it can e.-usily be seen that the maximum chord drawn, as 

 6 o is drawn is parallel to the line joining the centres P and Q.) 

 Hence the sides of the triangle PQK, are parallel to thoso of the 

 triangle a be, or P Q R like a fc c is equiangular, and therefore 

 is equilateral also. — Constant Reader. Your query .seems in some 

 way to have gone astray. We certainly put it in our box to forward 

 to the writer of electrical articles, but suppose it was not sent. — 

 BsiTANNlCfs. Would not the effect of the Saturday artillery prac- 

 tice be to produce heavy rainfall on Saturday and Sunday, if at all ? 

 Is there any evidence of a heavier average for these days ? Again, 

 the rainfall would be limited locally. Is there any evidence to show 

 that there is this local effect ? That under particular atmospheric 

 conditions heavy cannonading may bo followed by rainfall may be 

 true enough ; but " all great battles by land and sea " have not been 

 followed by heavy rains within twenty-fonr hours.— F. N. New- 

 coke. We might be able to find space for an occasional short 

 article on sulijccts connected with India, China, or Burniah, if 

 having a scientific bearing. Occasional notes on actuarial matters 

 would al»o be welcome.— S. Middleton. We have forwarded your 

 obliging commnnication to Mr. Haviland. who is now in yonr town. 

 — TKfTiiFtr. We may shortly have something to say on bicycles, 

 but for *oai'/i-txcrci«e the best use that can be made of a bicycle 

 is to exchange it for a good, light-running tricycle. Bicycle-riding 

 must Ijc regarded as the liold and clever achievement of a ilidicult 

 and hurtful feat. Consider the cramped, awkward, chest-com- 

 pretsing attitude of the most skilful bicyclists in riding, and note 

 how they walk, and you will sec that their exercise cannot bo good 

 for them. — W. S. BaofiK. Many thanks for your kindly and en- 

 cooraging letter. In part of our last issue the final result of the 

 Vienna Tournament was given. As we went to press before the 

 final ronnd wan over, yon can understand that the first copies could 

 not have it. — Lorekhith. Yonr answer to yonr question 2 

 ia qoiU; correct. As to the other question, the thing to be 

 proved is not true anieas n does not excee d a in a certain degree. 

 For instance, the integral part (it (v/a' + 1 + a)' is even when a^l 

 and n-10; I make it C72GO. go, again, when a- 2 and n-10, the 



integral part of the expressions is even — namely, lisGOSO. Your 

 rcjily to Pynuuus's question is not clear to me. Why should there 

 bo an increase of 180 each your, when it is obvious that after a few 

 years more than 12 will get their advance ? — Ed. P. Toy. No 

 conjuror who valued his repute would trust to a person choosing 

 '■ a lion " for animal, and " a rose " for flower ; as you say, 80 out of 

 100 would, even if that proportion really hold. But I'hnvo asked 

 many the question you suggest, and I find a much greater number 

 siiy "horse" and "dog" than "lion," and though "rose" 

 has a slight preference over other flowers, " daisy," " butter- 

 cup," and " heartsease," are chosen nearly as often, while 

 "pink," "wallflower," "violet," and "primrose," are not 

 far behind. I should say about a tenth choose " rose," 

 leaving the other nine-tenths for all the other flowers ; but cer- 

 tainly not so many as one-twentieth select " lion." Supposing the 

 chance one-tenth that a rose would bo selected by anyone taken at 

 random, and one-twentieth that a lion would be selected, the chance 

 that both would bo selected is oue-two-hundrodth, or there would 

 be 199 failures to one success. Taking even your numbers — 80 

 out of 100 for each— the chance of both being selected would 

 bo G,IOO ten-thousandths, or there wonld on the average bo 

 tliirty-six failures in 100 trials — far too many to leave a conjuror 

 a shred of reputation. — J. W. D. Chcrchili. Thanks ; but I doubt 

 whether so many take interest in the matter as you think. 



ELECTRICAL. 



A. Neal. l.The lumj) is constructed al'ior Swan's tlcsigii, but may 

 be only a catch-penny. Light is emitted by all parts of the filament 

 proper, but sometimes the connecting copper or platinum wires 

 extend some distance into the bulb. Apparently so in your 

 lamp. You can increase the candle-power by increasing the current. 

 2. RuhmkorfE induction coils can be procured at all prices, from 

 13s. or 14s. upwards. 3. We intend writing on secondary batteries 

 immediately. — P. C. F. The statement that, in driving a dynamo 

 by steam the UP is in inverse ratio to R, although at first sight 

 paradoxical, is quite correct when only E and R are given. HP is 

 proportional to EC, that is, is proportional to C, E being fixed ; bnt 

 C is inversely proportional to R, therefore UP is also in inverse 

 ratio to R. If C and R are taken, then, of course, HP is directly 

 proportional to R, C being constant, because E increases at the 



same rate that R does. Taking C'R= -jt- = CE, whichever of these 



identities is used, the result is the same. Virtually, C and E ai'o 

 the only quantities from which U P can be obtained. Inasmuch, how- 

 ever, as C and E are associated with R in the manner expressed 



by Ohm's Law ( C = jr-) i knowing any two of these throe quanti- 

 ties, we can readily ascertain the third. To simplify matters, suppose 

 we use a generator of low internal R, and whoso E is 50 volts, to 

 maintain incandescent lamps arranged in multiple arc. Then, if 

 each lamp offers, say 25 ohms, the current through each will be 

 2 ampt^res. Manifestly, the U P developed will bo directly as the 

 number of lamps, but the R will be inversely proportional (from 

 the law of parallel circuits). Joining the lamps in series will com- 

 pel US to increase the E as each lamp is added. C being kept con- 

 stant, the H P will be directly proportional to the R in the circuit. 



But in each case 



'H P. By taking several of numerical 



examples, and working them out, identical results will be arrived 

 at. — Alexander Howell. The colouration of phosphoric acid, 

 when dropped on your induction coil, was not due to electrical 

 action, but in all probability was the result of the chemical actiou 

 of the acid on the organic colouring matter used for dyeing the silk 

 or whatever else may be the substance of the insulating material. 



TUE TELESCOPE. 



Comet. — " Portable Equatorial " is a vague term — so vaftne, in 

 fact, that we cannot give a definite answer to your qsestion withour 

 you describe your form of mounting. In order to get at the Polar 

 region of the sky, your telescope ought to he mounted at one end of 

 the declination axis, being counterpoised by the declination circle 

 and a weight at the other. Of course, every equatorial stand (to bo 

 used as such) must bo a fixture, its Polar axis remaining, under all 

 circumstances, parallel to that of the earth. If you will be a little 

 more explicit in your description, wo will try to help you.^.T. W. 

 CofLBORN. No ordinary two-inch tele8C0|ie will bear a higher 

 power than 160, and it must be a very good one to perform well 

 with such an amount of amplification. In order to obtain thin 

 power on your own instrument, yon will require a Huyghenian eye- 

 piece, whereof the fdcns of the field-lens is 0-35 inch, and that of 



