♦ KNOWLEDGE 



[Aug. 28, 1885. 



(gossip. 



By Richard A. Peo^ 



Referring to part of " Hallyards' ' letter on " Magni- 

 fication near the Horizon," I may remark that whether the 

 mind does or does not unconsciously assign to the sky the 

 form of a flattened dome is a question which cannot be 

 disposed of quite so simply as " Hallyards " imagines. 

 The question how much farther away the horizon seems 

 to be than the point overhead, the sky being clear, was 

 put by Delambre, as one depending on precise laws of 

 optics — and the answer was " The horizon seems between 

 three and four times as far away as the zenith." The 

 idea of actual magnification, as an explanation, is absurd 

 on the face of it ; for if in a particular state of the air 

 the horizontal moon, really subtending — say — 30' when 

 not magnified, were made to subtend — say — 45', it would 

 follow that if there were 720 horizontal moons so placed 

 that if not magnified they would just make the circuit 

 of the horizon, then either, as actually seen through that 

 peculiar air they woiild overlap (which of course is 

 absurd) or they would more than go round, — once and 

 a-half round in fact — which is preposterous. (Of course 

 it is as easy to say that the dew or fog or rain may 

 magnify as it is to say that a body's velocity may pre- 

 vent it from yielding to the attraction of gravity, or that 

 under particular circumstances two and two might make 

 seventeen and a-half.) 



" Halltaeds " may not be aware that the constellations 

 seem to look larger near the horizon — but they cannot 

 really look larger, or they would not all get in. The 

 fact really is that an object can only seem to look larger 

 than usual, when not really magnified, through some 

 illusion which makes us imagine that the object is un- 

 usually distant. 



Me. Brothers has called my attention to an illusion 

 which is easily tested in illustration of this. Look at 

 some dark object on a light ground, and presently look at 

 a white surface at the same distance : you then see the 

 object light (and in complementary colour) and un- 

 changed in size. But if now you look at a distant light 

 surface, the image of the object seems to grow suddenly 

 larger. In reality it does not increase at all in apparent 

 size, but subtends — as of course it should — precisely 

 the same angle, being an unchanged retinal impression, 

 unchanged at least in extent. 



The apparent magnifying of the sun, the moon, star- 

 groups, comets, etc., near the horizon is in reality the 

 best proof we have that the mind unconsciously assigns 

 (as Delambre thought he had j roved it ought to assign) 

 a much greater distance to the horizon than to the zenith. 

 That this effect varies in degree with varying states of 

 the air shows that the mind unconsciously varies its 

 estimate of the horizon's distance according to the state 

 of the air. This may seem to some like arguing in a 

 circle. But you can argue safely in a circle when you 

 have facts all round. The fact that the moon seems to 

 look larger near the horizon, nay much larger (insomuch 

 that my small-disc method of measuring is by no means 

 rough for such a problem), while in the first place we 

 know from measurement that she does not subtend a 

 larger angle, and in the second place from the laws of 

 optics that she cannot be really magnified, is a good fact 

 to argue from. So is the fact that the horizon ought to 



be judged farther off, some 3J times, than the zenith. If 

 these facts correspond with each other that is only 

 because, being facts, they naturally "behave as such." 



Mv attention has been called by a correspondent who 

 wishes to be referred to as " L. E." (I should have pre- 

 ferred thanking him by name) to a singular mistake in 

 my last remarks respecting the Ruddy Eclipsed Moon. 

 I could scarcely believe I had made such a strange mis- 

 take till I referred to my article : but there it is ; and 

 rightly understood it is a mistake well worth Miss BallinV 

 attention as a singular mental phenomenon. 



I HAD explained, at p. 46, that the focus of a pencil of 

 raj-s from the sun after deflection through our earth's atmo- 

 sphere towards the moon lies far beyond the earth, — not {an 

 many, misinterpreting the investigation of the deflection 

 of the axesof suchpcn. :']=, 1,,,\-. f. 'ly imagined) between 

 the earth and the mi I 11, (iM! ii_'li, while of course 



my mind possessed t'\ • -■■'-■} "hicli this point is 



established, I wrote at p. 1 "- > (^i: li ilr of second column) 

 precisely as if — instead — I had known or proved, some- 

 where or somehow, that the focus of such deflected light- 

 pencils lay far beyond the sun, which is absurd, — even 

 taking along with this original absurdity the derived one 

 that the focus lies hundreds of millions of miles beyond 

 the sun. This of course was due to my setting the focus^ 

 as far relatively beyond the sun, as it really lies beyond 

 the earth. 



Partly as a penalty for my carelessness, partly perhap.-^ 

 to prove that I am not ashamed to acknowledge and 

 correct a mistake (venial vanity, I trust), and partly to 

 show that I had correctly considered the matter originally 

 at p. 46, I will now show how the position of the focu.s 

 for a pencil of rays leaving the sun's face for the edge of 

 the earth's disc (as seen from the moon) may be roughlj- 

 determined. The exact problem would be one of some 

 difiiculty, but we can get a rough solution by the fol- 

 lowing device. The breadth of the sun during central 

 eclipse is contracted, by the deflection of the axes of 

 pencils, to about 2| miles at the edge of the earth's disc 

 as supposed to be seen from the moon. (This supposes the 

 part of the sun's disc farthest from the rim of the earth 

 just lifted into view by grazing refraction, and the part 

 nearest the earth's rim lifted into view by atmospheric 

 layers about 2i miles above the sea-level.) Now this 

 shows that the bounding pencil-axes have their con- 

 vergence towards the eye of an imagined lunarian 

 diminished to about l-800th of what it had before 

 been. For when the earth is away the sun's disc 

 subtends at the moon about half a degree, corresponding 

 to about 2,000 miles at the earth's distance, and 2,000 

 miles exceed 2i miles 800 times. It follows (since tht- 

 lines of sight through the earth's atmosphere to different 

 points on the sun follow precisely the same course as 

 rays from those points to the eye from which the 

 lines of sight were taken) that the d'ivergence of a pencil 

 from a point of the sun to our earth's atmosjihere, to reach 

 the moon, is increased on the average about 800 times. 

 (On the average, because we have dealt with the con- 

 vergence after passing through the whole dejith of 2^ 

 miles : the eye-pupil can take in only a portion of each 

 pencil, a small fraction of an inch broad where passing 

 through the earth's atmosphere.) This being so, it 

 follows that the foci of such pencils lie on the averagi- 

 at a distance beyond the earth (as seen from the moon i 

 equal to about l-800th of the sun's distance,— say 



