Jdxe 29, 1883.] 



KNOWLEDGE ♦ 



395 



[iiixluct by 5, then add 12, aud, fiually, multiply by 10. Ho must 

 MOW hand to the performer the final product only, aud the performer 

 vill then instantiv toll him the tigurea ho originally chose. 



Thus, suppose the four liijures chosen wore — 



643,520 



Thus, the figures lianded to the performer, on 



a separate slip of paper, will be 543320 



From which ho will deduct privately 320 



5432 I 00 

 LeaWng, after cutting off the two last figures, 5432, the four figures 

 originally thought of. 



But then, it may be asked, whence gets the performer the 320 

 which forms, it would apjiear, the key to the trick ? The rough- 

 and-ready way of explaining this seems to me as follows : — We 

 must suppose the figures 5432 to be fast top links in a chain ; to 

 these the performer hooks a series of other links, to the number of 

 320 ; the deducting of the 320 is then simply the unlinking of the 

 chain, and the leaving of the four fast links as they stood at the 

 lommentement of the experiment. Thus x 2 = + 4 = 4x 5 = 20 + 

 12 = 32x10 = 320. Perhaps a more learned explanation of the 

 matter may easily be found by some of the scientific readers of 

 K.NOWLEDGE, but I give mine just for what it may be worth. I may 

 add, the same result may be attained by deducting 25 instead of 320, 

 slightly varying the preceding operations; thus, multiply the ori- 

 ginal figures by 2, then add 5, and finally multiply by 5 ; cut off 

 one figure only to the right, and the remaining figures will be those 

 thought of. Hero we get the 25 in the same manner as the 320 ; 

 thus, 0x2 = + 5 = 5x5 = 25. The first method, however, is, I 

 think, preferable to tlus latter one; being more complicated, the 

 trick becomes more mysterious — the great point at which the 

 conjurer should aim. G. M. 



[" G. M.'s " use of symbols is rather perplexing. What the per- 

 former really does is to niultiplv the original number (in this case 

 5,432) by 100, adding to it 4 x 5 + 12 x 10 or 320.— K. P.] 



VACCINATION. 

 [859] — I was rather vexed to see in your journal figures ex- 

 tracted from the Medical Pres.^ which are so wrong. Mark, now, 

 how a plain tale shall put yon or them down. 



108 certified deaths vaccinated is 25 per cent., not 37, 

 to which add ■' doubtful," as only a small proportion 

 of the population are unvaccinated. 

 184 42i per cent. 



292 Deaths of vaccinated G7i „ 



139 Remainder unvaccinated 32i „ 



431 100 



I think the above the more accurate representation of the 

 Cgures. Chas. Johnson. 



[Perhaps; but why interchange the "doubtful" (139) and the 

 "unvaccinated" (184). In the Medical Press, the percentage was 

 considered only on the undoubted cases, which, as I pointed out, 

 was not a correct way of dealing with the matter. The actual 

 numbers and percentages are : — 



Number. Percent. 



Vaccinated 108 25 



Unvaccinated 184 42^ 



Doubtful 139 32i 



100 

 If we add all the doubtful cases to the vaccinated, wo get 57i per 

 cent, of the deaths among the vaccinated. But you must bo a most 

 energetic ;idvocate of vaccination to suggest this. Do you not see 

 what you are doing ? You are assuming that so small is the pro- 

 portion of unvaccinated folk, that among 139 doubtful cases (or 

 say, even 184), not one was probably anvaccinated. It follows. 



according to your reasoning, that the vaccinated are nearly two 

 hundred times as numerous as the unvaccinated ; yet, instead of 

 supplying nearly two hundred times as many deaths (or 184 

 for 1), they only supply about four deaths for three (or 84 for 138) 

 among the unvaccinated. The most ardent advocates of vaccina- 

 tion do not claim greater protective effect for vaccination as at 

 present managed. — H. P.] 



ON THE FORMATION OF COMETS' TAILS. 



[860] — The supjiosition that an active tail-forming comet is made 

 up of meteoric masses, some of which consist almost entirely of 

 matter volatilisable by the sun's heat, is in no degree invalidated by 

 the fact that meteors consisting of such volatile material never fall 

 to the earth. 



Though it is probable that any of the matter now contained in 

 the meteoric streams which the earth encounters in her path round 

 the sun once formed part of the material of a comet, this matter 

 must have long since parted with any volatile matter with which it 

 may then have been associated. 



The meteoi ic stones, therefore, which reach the earth must be 

 regarded as affording evidence as to the nature of the non-volatilo 

 material only which a comet may contain. The earth would have 

 to pass through a comet, probably quite close to its nucleus, before 

 it could encounter masses of volatilisable matter. Prom my view, 

 it is only masses of moderate size which could be carried away 

 from the nucleus by the steam of gas setting outwards from it, 

 and be afterwards ejected by the evaporative force into the tail ; 

 and such musses could not long bo exposed to solar radiation in 

 vacuo without quickly losing by evaporation all their volatile 

 matter — probably before they had been carried very far into the 

 tail. 1 speak of the evaporation as taking place in vacuo, for I con- 

 ceive that when a meteoric mass has been ejected to some distance 

 from the nucleus, the evaporation will take place in what may bo 

 regarded as an almost absolute vacuum. 



I may again state that I nowhere advocate the view which Mr. 

 Kanyard persists in attributing to me, that the volatilisable matter 

 of a comet is ice. Nor is it at all essential to my view that the 

 dimensions of the evaporating masses should be as largo as a cubic 

 metre. It will be seen from the formula I have given that the 

 ultimate activity attained by the comi)lete evaporation of the 

 volatile portion of a mass depends only on the proportion which 

 the volatile portion bears to the non-volatile portion, not on the 

 absolute dimensions of the mass. There would, however, be a 

 point at which the formula would not be strictly a))plicable, for, 

 when the mass has become reduced by evaporation to an 

 exceedingly small particle, the effect of the solar rays, in 

 causing evaporation, could hardly be confined^ to one side only 

 of the particle. I believe, however, that the particle might 

 be reduced to verj- small dimensions before the solar heat would 

 cause evaporation on both sides, for experiments on evaporation in 

 vacuo appear to indicate that radiant heat, falling on an evaporating 

 surface, is almost entirely spent in producing evaporation, and that 

 very little heat is carried by conductiou into the intorior\)f the 

 evaporative body. As the polarisation of the light from a comet's 

 tail points to the conclusion that the bulk of each evaporating mass 

 after evaporation is very minute, it will not bo necessary to suppose 

 it to have a large bulk before evaporation, in order to account for 

 its velocity tailwards. 



In conclusion, I would remark that Mr. Ranyard, in his communi- 

 cation to Knowledge for May 18, has not attempted to refute the 

 argument by which I showed that the particles of mist which he 

 supposes to form the tail of a comet could never acquire a velocity 

 greater than the average velocity (duo to their thermal energy) of 

 the molecules of gas evaporated from them, though he still 

 adheres to his opinion that the particles, by continually picking up 

 fresh matter, and evaporating it again towards the sun, would be 

 continually acquiring fresh velocity, and might ultimately acquire a 

 velocity sufficient to account for the tail formation which, if my 

 argument be valid, is out of the question. A. S. Davis. 



Cheltenham, June 11, 1883. 



COMETS' TAILS AND THE SUN'S SURFACE. 



[861] — In an article of mine, published in " yours " of Fob. 2nd 

 last, I endeavoured to show that comets' tails might bo considered 

 to bo formed by a repulsive force acting with an intensity varying 

 as the surface exposed, and so in small condensed particles over- 

 coming gravity, which acts according to mass, i.e., in bodies of a 

 given density a function of the volume. I also supjiosed that this 

 repulsive force was a molecular bombardment similar to that which 

 takes place in a Crooke's Radiometer. I did not answer Mr. Ranyard 

 and others. I derived profit from their contributions, and my 

 own views were in a transition state. I now seek to inquire 



