Oct. 9, 1885.] 



KNO^VLEDGE ♦ 



307 



us after geometrical sunset is completed,* this, which is 

 really shown by the above explanation, remains with 

 many a matter not only hard to see, but actually to be 

 denied as absurd on the face of things. 



The difficulty commonly presents itself in this way. 

 If by the bending power of the earth's air rays from a 

 particular part of the sun's disc are deflected to the 

 moon, then rays from another part of the sun's disc must 

 be deflected away from the moon ; how then can all parts 

 of the sun's disc bo visible from the moon ? Added to 

 which comes another difficulty, based on a different mis- 

 apprehension, — If light from every part of the sun 

 reached the moon she would not be in eclipse at all, but 

 shine as brightly as ever. 



Let us see how the matter really is : — - 



Suppose first that s a is a ray from the lowest point s 

 of the sun S (lowest considered with reference to the 

 figure) to the earth's atmosphere at a and so deflected as 

 to pass to the moon at M. Then it is obvious that a ray 

 s'a from the highest point s', will be carried as to m, and 

 not reach the moon at all. But a ray from s' to some 

 point b' in the atmosphere above a, will be deflected 

 precisely to M. Thus an eye placed at M would see the 

 part s' of the sun in the direction M &', and the part « in 

 the direction M a, and all intermediate points on the 

 face s S s in directions intermediate to M a and M b. 

 Thus the diameter of the sun's disc from s to s' (the 

 semicircle s S s' in reality would be transformed into a 

 short straight line a b' on the edge of the earth's disc as 

 seen from M. In like manner the same diameter of the 

 sun's disc would also be transformed into a short straight 

 line a'b on the opposite edge of the earth's disc, by rays 

 following courses ranging from s' a' M to s b M. Imagining 

 the plane of the figure to revolve on the straight line 

 S E M, we get the same result for every diameter of the 

 sun's disc, — or the sun transformed into a ring around 

 the earth, in the manner already dealt with (all but these 

 preliminary and I had supposed nearly obvious con- 

 siderations). 



Here we have supposed the moon in apogee. If she is 

 nearer the earth the point s on the sun will not be 

 rendered visible by refraction at a, which would carry it 

 above the moon. A ray from some point p, near to s 

 would be so carried, and the arc p S s' would be visible at 

 a transformed into a straight lino as ii b', while a cor- 

 responding arc p' S s would be visible at a transformed 

 into a straight line as a' b. The wliole sun would be 

 visible, but not evcrj part of the sun doiibly visible as in 

 the former case. 



These rays thus falling on the moon are rays of actual 

 sunlight, not different from the rays by which wo see 

 the setting sun except in having some of them traversed 

 a greater range of terrestrial atmosphere, and so having 

 suffered more absorption, and making the ring into which 

 the sun is transformed or distorted look, at least along 

 its inner edge, much ruddier than our setting sun usually 

 looks. I say " some of them," because clearly the rays 



3 globe has 



which like s' b' M have only traversed the higher regions 

 of our air would not suffer absorption in anything like 

 the same degree. 



And here, in passing, let me remark that Mr. Ran- 

 yards idea that the parts of our air above the highest 

 range of clouds may be (or as he suggested must be) the 

 parts chiefly acting in carrying sunlight to the moon 

 duriuo- tnlal crli|.„., is inwlmissible. The refractive 

 powir . r ;iir i> iKMily jiroportional to its density. At a 

 heiiflii 'if .'I'l iiiiliv^ 1 lie air will not deflect the sun's rays 

 more than :i\\ us aln'udy mentioned, and in central total 

 eclipse this wouhl not suffice to bring a ray of sunlight 

 to the moon. For, as supposed to be geometrically 

 measured from the moon (one cannot say "seen " because 

 it would be hidden), the edge of the sun's disc at the 

 time of central eclipse would be more than 40' from the 

 edge of the earth's disc. Probably the highest part of 

 the air effective at that time in bringing the sun into 

 view would be not more than two and a half miles above 

 the sea-level, and it could not be more than three miles. 

 Clouds float much higher than that. If further proof 

 were needed, it would be found in the raddy colour of 

 the eclipsed moon, which shows that usually the light 

 she then receives has traversed the lower strata of our 



This in reality is a sufficient solution of the problem 

 of the ruddy-eclipsed moon. At least the solution is 

 sufficient when combined with such an inquiry into the 

 amount of illumination which the moon would receive, 

 as I gave in former papers. What else I then wrote was 

 chiefly an elaboration of the necessary part of the ex- 

 planation, by an investigation of the actual nature of the 

 distortions of detail which the sun's face would undergo. 

 (To be concUuU'd l?i our next.) 



OPTICAL RECREATIONS. 



By a Fellow of the Royal Astronomical Societt. 

 (_Contimtcdfrotii2>. 270.) 



SO far we have only spoken of light and darkness as 

 the results of polarisation. It remains briefly to 

 touch upon the gorgeous chromatic phenomena exhibited 

 when light thus altered in its character traverses certain 

 minerals and organic substances. We will, first of all, 

 say something of the phenomena themselves, and then 

 endeavour to afford, very shortly indofil, ;is luucli nf an 

 explanation of their cause as can be givtu witlimit the 

 employment of mathematics. The mineral known as 

 Selenite will supply us with material for tlic I'xpiriments 

 we are about to make. It is the cr3-stalline form of 

 gypsum (from which Plaster of Paris is m;wle by burning 

 it). Crystals of it are very common in the London clay 

 of the Isle of Sheppey, whence we ourselvis have obtained 

 numerous specimens. Very well, then : obtaining 

 one of these crystals we .shall find that it is of a slab- 

 like form, and is made up of innumerable thin plates, 

 which may be split off with a sharp penknife. Let us 



that the rhombs in Ki,'. 17, tho lounu;" 



vy 



Pig. I'J A, it w,ml,l In. put lln-ou-h tlu- slit S, squar 

 to the axis of the tin cyliiulor), and upon now lookin 

 through the second rhomb or slice of tourmaline, ( 



