no 



- KNOWLEDGE ♦ 



[Aug. 17, 1883. 



the cii'culai* sectiou aud cousequently the cubic contents of the 

 pillai' conld be obtained. 



Now, imaj^ino the pillar to become very extensively dwarfed, so 

 as to meet the requirements of the parcel post ; its length to be 

 3 ft. 6 in., and its girth consequently 2 ft. 6 in., so that the two are 

 together ft. Proceeding as before, we should get the diameter of 

 the circular section very nearly 10 in. If, then, we conceive a 

 cylindrical parcel about a yard in length, and each end about the 

 size of a dinner-plate (10 in. in cUameter), this will represent the 

 required limits. 



When the parcel is shaped like an ordinary box the girth becomes 

 twice the breadth and thickness together; or, if the section be 

 square, four times the edge of one end. The longest box, then, that 

 can be sent is one 3 ft. 6 in. in length, and the edge of whose end is 

 7iin. 



If the box be of cubical shape the length of its edge must be 

 one-fifth of ft. ; or about 1 ft. 2 in. ; and this is the greatest-sized 

 cubical box that can be sent. 



It may be shown by the differential calculus that the largest 

 content to be got out of the box shape is when the dimensions are 

 2 ft., 1ft., 1 ft. or two cubes of 1ft. placed face to face. For the 

 cylindi'ical shape this becomes length 2 ft. (as before), and girth 

 4 ft. giving a circular section of about 15 in. diameter. 

 R. F. Davis, M.A., 

 Cambridge, Queen's College ; Member of the 

 London Mathematical Society. 



AUDITORY FANS. 

 [808] — The fans, &c., spoken of in your answers to correspon- 

 dents under C. Thompson, are sold with all particulars at a shop 

 next door to St. Saviour's Deaf and Dumb Church, 419, Oxford- 

 street. Xox. 



THE VORTEX-ATOM THEORY. 



[899] — The vortex-atom theorj', viewed from the physical side, 

 is regarded by some as one of extreme simplicity. I must confess, 

 however, that to me it appears to be far otherwise. In fact, I am 

 unable to understand how the theory is to be reconciled with the 

 first law of motion. According to that law no body possessing 

 inertia can deviate from the straight line unless forced to do so. A 

 planet will not move round the sun unless it be constantly acted 

 upon by a force defiecting it from the straight path. A grindstone 

 •will not rotate on its axis unless its particles are held together by a 

 force preventing them from flying oft' in a tangent to the curve in 

 which they are n:ioving. Centrifugal force must always be balanced 

 by centripetal force. My diificulty is to understand what force 

 counterbalances the centrifugal force of the rotating material of 

 the vortex-atom. It has been said that the centrifugal ten- 

 dency of the rotating material of the vortex-atom is con- 

 trolled hy the exterior incompressible liquid. But it is also 

 stated that this incompressible liquid offers no resistance 

 whatever to the passage of the atom through it. In short, that 

 in so far as the motion of the atom is concerned this liquid is a 

 perfect void. Now, if this Kquid can offer no resistance to the 

 passage of the atom as a whole, how then does it manage to 

 offer such enormous resistance to the materials composing the 

 atom so as to continually deflect them from the straight path and 

 compel them to move in a curve ? The centrifugal force of these 

 vortex-atoms must be enormous, for on it is assumed to depend the 

 hardness or resistance of matter to pressure. Now the centripetal 

 force which balances this centrifugal force must be equally 

 enormous. Then if this perfect fluid outside the vortex-atom can 

 exert this enormous force on the revolving material without being 

 itself possessed of motion, then there does not seem to be any 

 necessity for vortex-motion in order to produce resistance. 



It has further been advanced, by way of explanation, that this 

 incompressible liquid surrounds the revolving liquid like a pipe, 

 "and that if the liquid in this pipe were to fly out, a temporary 

 void would be formed in it, which is impossible in a liquid that 

 already occupies all space." The incompressibility of the surround- 

 ing fluid sui-ely cannot be a reason why portions of the revolving 

 material do not fiy out, for if incompressibility could prevent 

 portions of the revolving atom from flying away, it would equally 

 prevent the whole atom from doing so, but according to hypo- 

 thesis this incompressible fluid offers no resistance to the motion of 

 the atom. When the atom moves it is assumed that the fluid in 

 front is dis]jlaced ; but then this simply makes room for an equal 

 quantity behind, and thus no void is formed. The very same thing 

 ought to take place, though only a portion of the atom were to fly 

 off. The various portions of this revolving material are not 

 supposed to be held together by any cohesive force like those of 

 the grindstone. What then prevents the revolving material from 



being dissipated by the centrifugal force of rotation 'i* In short, 

 how is the existence of the atom possible under the physical con- 

 ditions assumed in the theory ? James Ceoll. 



LETTERS RECEIVED, AND SHORT ANSWERS. 



L. A. B. — The small magnets would very speedily have their 

 polarities reversed by the more powerful fixed magnets, and resist- 

 ance to rotation would ensue. Supposing, however, that the 

 polarities were unaffected, the action would be in character with 

 that which would result if a diamagnetic substance were substi- 

 tuted for the small magnets — that is to say, resistance to motion 

 would evidence itself. It will be seen that although repulsion 

 would be exerted upon receding and approaching magnets 

 equally, resistance to motion would be experienced owing to 

 the "squeezing" effect exerted upon the magnets between the 

 fixed poles — S. Qcint. If wo had a telescope of the power 

 you mention, the movements of Jupiter's surface would un- 

 doubtedly be magnified in the same enormous degree, and 

 unless the effect of his rapid rotational motion were corrected 

 there would be a rapid rush of the featm-es across the field 

 of view, with the blurring you speak of ; but it would be the 

 easiest thing in the world to correct this by the use of clockwork, 

 keeping the telescope directed to a fixed point on any zone. In that 

 case there would be no blurring at all. — E. A. Rowe. I am no 

 arbiter of literary tastes. Nearly all the works you mention are 

 popular. — F. Pitman. Have not seen the former work. A notice 

 such as you send me would imply that I had and approved of 

 it. — Geo. Joedak. What ivill you ask next? You want me 

 now to explain why the moon is always full in the Arctic 

 regions, why she never sets there, — and again you ask, "Can 

 it be possible that there is a south pole as well as a north pole and 

 the moon when crescented goes round the north centre and when 

 at full she goes round a south centre ? " And yet again, when I say 

 the moon is every month half the time north of the celestial 

 equator and the other half south, you " suppose in that case," I 

 "refer to the month of June especially and only in June." (Now, 

 is June every month ?) Will you permit me to inform you, once 

 for all, that the moon's behaviour in both the Arctic and Antarctic 

 regions is precisely the same so far as her apparent form is concerned 

 as it is anywhere else. When the moon is full here she is full 

 wherever she can he seen, when gibbous gibbous, when crescent-shaped 

 crescent-shaped. The moon is seen in the Ai'ctic regions (and here, 

 be it noticed, I am speaking of places well within the Arctic 

 circle, not upon or just within it, but say north of seventy-two or 

 seventy-three degrees) during part of every month, the particular 

 part of each lunar mouth in which she is best seen varying as the 

 year goes round. In December she is full when highest above the 

 celestial equator, and consequently she is then visible as a full moon 

 all through the night. In high Arctic latitudes she is visible in 

 December all through the night from a few days before full to a few 

 days after full. In January the part of the lunar month when the 

 moon is seen all night ranges over a week or so, in high latitudes, to 

 about the time when she is full. In Febraary the week during the 

 lunar month when the moon is visible all through the twenty-four 

 hours ends a few days before the time of full moon. In March it ranges 

 equally on either side of " half-moon before full." In April it cuds 

 at about the time of half-moon before full ; and in May a few days 

 earlier. In June there is no night, at least towards the end of 

 the month; and at this time the moon is only risible above the 

 horizon all through the tweuty-four hooi-s when near the sun or 

 appearing as a fine crescent. She is invisible all through the 

 twenty-four hours when nearly new in December near the time of 

 midwinter ; for about a week, ending at time of new moon, in 

 January ; a few days earlier in the lunar month in February ; for a 

 week equally divided ou either side of half-moon after full in March ; 

 for a week ending at about half-moon after full in April ; 

 and a few days earlier in the lunar month, in May. The moon 

 is invisible all through the twenty-four hours when nearly full near 

 the time of Midsummer — in high Arctic latitudes — i.e., four or five 

 degrees north of the Arctic circle. You should find no difficulty in 

 extending these considerations to the remaining months. Again, 

 for the Antarctic regions, you have only to write July, August, 

 September, October, November, and December, resi)cctively, for 

 December, January, February, March, April, and May, in the pre- 

 ceding account, to have a correct description of the phenomena 

 there. You are bound to tell me that some of your old captains deny 

 all this, and say the moon is always full in the Arctic regions, never 

 sets there, can be seen full in high arctic latitudes at midsummer, 

 and so forth. But besides these old captains there have been, let 

 me remind you, sundry old Arctic captains not altogether un- 

 known to fame, such as Sir E. Parry, Sir Jas. Ross, McCIin- 

 tock, and a few others, who have not — like yours — tried 

 to recall, with obviously imperfect memories, what they 



