290 



♦ KNOWLEDGE ♦ 



[April 3, 1885. 



there would be very little of that opposition which now exists. 

 There are unreasonable people among the anti-vivisectionists, but 

 their number would be very small indeed was it not known beyond 

 a doubt that a great many physiologists in this country would, were 

 they granted an inch, be only too ready to take an ell. 



I will do the non-professional supporters of thest. men the justice 

 of saying that I am certain that few, very few, of them have the 

 remotest conception of what this ell would be. 



Boyd Mo.ss, F.E.C.S. 



[Will Mr. Moss kindly point out where, either on p. 243 or any- 

 where else, I hare ever advocated "unlimited physiological 

 research" ? I am at least as much alive to the wickedness of the 

 ghastly cruelties perpetrated by .Schiff and others as he can pos- 

 sibly be ; but est nivjiis in rchitx, and our correspondent must know 

 full well, if he will only study 39 and 40 Vic, c. 77, with the 

 slightest attention, that the repetition of such experiments as-those 

 by which certain Continental physiologists have disgraced them- 

 selves is impossible in England. To say, because enormities have 

 taken place elsewhere, that hence English men of science shall be 

 deb.arred from making physiological experiments altogether is to 

 parody the teetotalers' argument, that because Mr. Sykes gets drunk 

 and jumps with his hobnailed boots on the prostrate body of the 

 unfortunate creature he lives with, hence I am never to take half- 

 a-glass of sherry again as long as I live. — Ed.] 



THE NAKED TRUTH. 



[1657] — It seems singular there should be any dispute (letter 

 1645 et ante) respecting the power of men to live naked, not only 

 in a temperate, but in a very inclement climate, in view of the 

 testimony of our late great naturalist. 



In his'" Voyage of II. M.S. Beajle Round the World," page 213, 

 edition 1870, Mr. Darwin, after describing the scanty garment of 

 the central tribes of Fuegians — a small scrap, about the size of a 

 pocket-handkerchief, hardly sniKcient to cover the back so low 

 down as the loins — continues : — " But these Fuegians in the canoe 

 were quite naked, and even one full-grown woman was absolutely 



so." " In another harbour, not far distant, a woman, 



who was suckling a recently-born child, came one day alongside the 

 vessel, and remained there, out of mere curiosity, whilst the sleet 

 fell and thawed on her naked bosom and on the skin of her naked 

 baby." 



At page 218, he gives an instance of four or five men suddenly 

 appearing on the edge of a cliff " absolutely naked," their long hair 

 streaming about their faces. On another occasion, a small family 

 of Fuegians having joined his party round a blazing fire, he says : — 

 "We were well clothed, and, though sitting close to the fire, were 

 far from too warm ; yet these naked savages, though further off, 

 were observed, to our great surprise, to be streaming with perspira- 

 tion, at undergoing such a roasting" (p. 220). 



Cecil Du.xcombe. 



SUNDIALS TO SHOW MEAN TIME. 



[1658] — Old globes and maps of the world used to contain a 

 gi'aphic table of the equation of time, in the form of a curve called 

 an " analemma," like a lengthy, slightly-leaning figure 8, touching 

 with its larger bow the southern tropic, and with its smaller the 

 northern. The two points where it crossed any parallel were 

 distant from its main meridian by the sun's difference from clock 

 time at the two moments of the year that his declination corre- 

 sponds to that parallel. Thus, the whole curve represented the 

 course of the sun's centre during a year, relatively to the imaginary 

 mean sun's centre, or to one going round the ecliptic with uniform 

 speed, or on one identical meridian mounting and returning from 

 one tropic to the other and back. 



Now, this figure might bo projected on a cylinder, or Mercator's 

 Chart, as well as a globe ; and its degrees each way from the 

 equator, instead of being equal, must then increase like a scale of 

 tangents up to 23J^°. The whole problem of making a dial show 

 clock-time then resolves itself into making, as gnomons, two solids 

 of revolution that can cast shadows whose outlines are each one- 

 half of this 8-like figure, one to be used while dsiys are lengthening, 

 and the other while they are shortening. But each solid must have 

 every part of its surface conve.i, and, as it has to receive the sun's 

 rays not perpendicularly to its axis (except at the equinoxes), but 

 inclined at all angles down to 66^° each way, the shadow to be 

 taken into account is not one cast by the sun, but by a single 

 luminous point, so near that the gnomon's length subtends 47° 

 thereat. 



Wo may take any meridian line through the 8-like curve (half of 

 the 8) as the axis of the solid, provided it be not so far from the 

 mid-breadth as to make part of ( no of the bulbs concave-necked (as 

 it will be if the other bulb either vanish or be very small). It is. 



therefore, safest to choose such an axis as makes the two maxima 

 of width, in the north and south bulbs, nearly or quite equal. As 

 the meridian doing this will not be that on which the mean sun is 

 supposed to remain, the XII. of the dial scale will not be at the 

 true meridian, but shifted as much as we have shifted the line that 

 wo make the axis of our gnomon. 



This makes my old suggestion of unshipping and changing the 

 gnomon twice a year, on one identical dial, very inferior to that of 

 having two dials separate. 



Take first, then, that for lengthening days (I mean lengthening 

 in the north, for our dial will do equally for cither hemisphere). 

 During the sun's north-coming, his time varies between 14m. 283. 

 behind clock, and 3m. 52s. before it. The mean of those is 5m. IBs. 

 behind clock ; and this equation occurs when his declination is 

 2" 51' N. So, by shifting the scale of the dial 5m. 18s., we can 

 have a gnomon whose bulbs are of equal width, but the waist 2° 51' 

 north of the equator. 



For the other, during the sun's south-going, his time variea 

 between 6m. ICs. behind clock, and 16m. 20s. before it. The 

 mean of those is 5m. 2s. before it ; and this occurs at nearly the 

 same declination as the former, 2° 48' N. Therefore, this gnomon 

 will have its waist like the other, practically at 2° 50' N., and 

 hardly visibly differ from it, though both bulbs are slightly bolder. 

 But this dial scale must be shifted 5m. 2s. the contrary way ; so 

 that the two dials will differ by 10m. 208. 



Taking from half the Naufieal Almanac, p. 1, of each month, any 

 number of declinations and the corresponding ecjuations of time, 

 you must add to each of these the corresponding "mean-lime of 

 sun's semi-diameter passing meridian." Then you have the ordi- 

 nates for what I will call the electric shadoie-ciin-e of one gnomon, 

 to be used from solstice to solstice. The corresponding abscissae 

 are the tangents of each declination. But you want the solid of 

 revolution that will cast such a shadow, when illumined by a very 

 small electric light of the brightest kind, so near that its length 

 subtends 47° from that light. To make the section of this, you 

 must take the sines of those same angles of which the shadow-curve 

 had the tanijents, and apply the same ordinates to each. Thus yon 

 .see the curve of the gnomon itself, or of its sun-shadow, differs 

 much from the old " analemma " curve, which is that of its electric 

 shadow. 



The width of the waist of each gnomon will coiTespond, on its 

 dial scale, to the mean time of sun's whole diameter passing, 

 when his declination is 2° 60' N., which happens to be the least time 

 that passage ever takes — namely, somewhat under 2m. 10s. By 

 giving the waist this width, the black shadow will there exactly 

 vanish, or its outline become a true figure of 8, the curve crossing 

 itself. Now, you may ask, how arc we to insure the use always of 

 the right half of this figure, that is, on one half-year's dial the right- 

 hand side of lower bow and left-hand side of upper, but on the other 

 dial the right-hand side of upper bow, and left hand of lower ? 

 Nothing is easier. Attach to each bulbous swelling, on the side 

 that must not be used, a tangential plane strip of thin metal in- 

 dented like a comb or fringe. As no single dial is to be used 

 longer than nine hours, the shadow of this fringe will always make 

 one side of the gnomon's shadow plainly not the one to be noticed. 



The "analemma," figure of 8, generally an italic one, was 

 %iprijht six centuries ago, when the difference of its bows was a 

 maximum, and then one gnomon and dial would have done through 

 the year. Some forty-six centuries hence that will again be the 

 case, but the bows equal as well as upright. Their inequality is 

 decreasing since the thirteenth century, but the leaning, that 

 necessitates two dials, increasing for the next twenty centuries; 

 then to decrease for some twenty-six, till they are both upright 

 and equal, as fifty- eight centuries ago. E. L. G. 



P.S. — I was wrong about the gnomon curve, which cannot be 

 plotted, I fear, in any way. But something can be turned in a 

 lathe, beside an electric light, till it casts the required shadow. 

 The divergence must be just 47'. A sunbeam admitted through a 

 lens that would servo for a telescopic eyeglass (either convex or 

 concave), will do as well as an electric arc. The gnomon curve 

 does not differ so much from its electric shadow as I thought, but 

 is a " tough 'un " for mathematicians. 



The gnomons are too thin-waisted to be made solid, but could be 

 electrotyped hollow, and sustained by a strong wire stretched 

 tightly through their .axis. 



ATWOOD'S MACHINE. 

 [1630] — Your correspondent " W. G. W." is wrong in supposing 

 there to be any error in the expressions for/ (the rate of increase 

 per second in the velocity of the descending mass) given on page 58 

 of Williamson and Tarletou's "Dynamics." Supposing the moving 

 mass constant, the acceleration varies as the pressure, or statical 



