306 



♦ KNOVV^LEDGE 



[Oct. 9, 1885. 



from every p.irt of the sun reacli nearly the whole of the 

 moon's surface even then), that in point of fact the sun 

 would be absolutely visible, though distorted, from every 

 part of the moon's surface at the time of central total lunar 

 eclipse, is regarded as incredible. Yet it is the simple 

 truth. 



This is precisely the fact which I not only took for 

 <i;ranted, bat which I treated — in my former papers — as a 

 fact which should be obvious to every one likely to be 

 studying this subject at all. The only difficulty I could 

 see — in fact the only difficulty there is, but it is much 

 more troublesome than I imagined — is a difficulty 

 which would quite as much trouble an unsound reasoner 

 in trying to determine whether the sun would be visible 

 through the effects of refraction after he had really set 

 in the geometrical sense. If we did not actually see the 

 sun in this way, I imagine we should find many persons 

 capable of clearly proving that the sun could not be so 

 seen, or only by a very small portion of his light. One 

 of these — misapprehending perhaps an explanation by 

 Sir John Herschel — might reason thus : — 



Fig. 1. 



Suppose H E to be the plane of the horizon, and piit 

 HA to represent the air at H (it is a little wild to 

 represent the air by a straight line, but Herschel, who 

 unfortunately seems to have had little skill in planning 

 diagrams, represents the earth herself by a straight line 

 in the corresponding part of his explanation of the ruddy 

 eclipsed moon) E, the eye of an observer. Then if a ray 

 S A from the sun S below the horizon is refracted in the 

 direction A E, it will reach the observer at E, but only 

 just that ray ; for a ray S a will be refracted to e far on 

 one side of him, and a ray S a! will be refracted to e' far 

 on the other side of him. Therefore he will get but the 

 merest fraction of the sun's light, and to say that he will 

 .actually see the sun, (apart from atmospheric absorption) 

 as well as if the sun were above the horizon is absurd on 

 the face of it. And so forth. 



Only, as a matter of fact we see the sun, and so this 

 false reasoning never gets fairly started, — as the cor- 

 responding false reasoning about the ruddy eclipsed moon 

 very naturally has been. 



Now let us consider the real facts iu regard to the 



Fig-. 2. 



Let the lines in Fig. 2 be supposed to represent rays 

 coming from a point on the sun, very far away on the 

 left to the earth E and the moon M at the time of total 

 eclipse. The rays which come through the atmosphere 

 at a and a', just touching the earth are bent through an 

 angle of about 3-t' as they enter and as much as they pass 

 out, so that they are deflected through an angle of about 



68' in all and cross at a point as c which lies on the line 

 E M, not far from the moon M, because the angle o M E 

 (or more precisely because the angle whose sine is E a -^ 

 E M) is only about 58', whereas the angle a o E is about 

 68'. Rays which pass higher up, as at h and h' are de- 

 flected less, and cross as at c', on E il produced, farther 

 and farther ;i\vay till we get no deflection at all and the 

 r.iys siiii |'1\ I ill lie on straight lines diver^aug fr.im the 

 parti- I : " : , thesun weare consiileriu-. If fi, V, 



ai-i' ;i ' 'i I miles where the atmospheric density 



is r.'lii' I r li ill, the deflection will b? about one half 

 what it is at the sea-level, or the angle & c' E about 34°, 

 so that rays travelling so high in our air would pass 

 considerably bey<md the moon when she is situated as 

 shown in Fig. 2, supposed to correspond to the time 

 when the particular point on the sun considered is 

 just centrally beyond the earth supposed to be seen from 

 the moon. 



So far we have what Sir John Herschel has pointed 

 out, in the passage whose full meaning has been so 

 strangely misunderstood. The moon at M gets but a 

 small proportion of the rays carried around the earth in 

 the way shown. In fact as we know that she subtends 

 about 32' as seen from the earth, she only gets those rays, 

 of the particular set illustrated above which are deflected 

 within 16' on either side of 58', — that is, which are 

 deflected between 42' and 68' (none are deflected between 

 68' and 74', the necessaiy angle to just reach the lower 

 edge of the moon from near a and the higher edge from 



If we suppose rays from the middle of the sun's disc 



(as seen from the earth or moon) dealt with in Fig. 2, it 



is easy to make the same figure by a slight addition 



illustrate the case for rays from points on the edge of 



that disc. For a line from the edge to E (that is, 



from either point on the edge of the solar disc in 



the plane of our figure) would be inclined either 



in direction E w or 'Em', where the angle wEwi 



(bisected by E M) is the angle subtended by the 



sun's disc. We shall be near enough to the truth in 



putting m and m' on the outline of the moon at M. Then, 



instead of encumbering our figure and our minds by 



I drawing a complete set of rays for each or for either of 



I these directions, all we need do is to regard the set of 



I rays already drawn as corresponding to either case, and 



setting a moon at tti and at m' as shown. For either of 



these moons, the case is illustrated in which the par- 



1 ticular point on the sun's surface dealt with lies at 



the edge of the sun's disc as seen from the earth or 



Now in reality this — so far as a general explanation of 

 the illumination of the moon's surface during totality is 

 concerned — ought to be enough. Sir John Herschel was 

 content to give even less in the way of explanation and 

 illustijation. Yet he showed clearlj' enough all that is 

 really essential. 



But strangely enough this explanation has been 



altogether misapprehended. It has been supposed to 



show that the moon can receive scarcely anj- light from 



the sun by the actual deflection of solar rays towards her, 



■ that the light thus received counts for little or 



!ompared with such illumination as the moon 



-roin oiiv te-rr,sirial twili-ht tj-low. from the 



\ nothin 



burnishinLT of i 

 nation. Tl ' 

 2, the sun l.pi 

 reduced in aj'p; 



which is seen, f 



rcui siiu iluii mucu ic^a noki than usual 

 1, but still that it is his very own self 

 s certainly as the setting sun is seen by 



