Jdly 24, 1885.] 



KNOAVLEDGE 



indeed Mr. Ranyard has partly indicated, the degradation 

 of light is more rapid as the earth approaches S, because 

 not only are the crescents of visible disc diminishing more 

 and more rapidly, but the average lustre of the visible 



portion is also rapidly diminishing. If vre drew, as in 

 Fig. 2, a diagram, such that, OX and O T being axes, 

 C, K, L, and M represented the breadths S C, 

 SK, SL, and SM of Fig. 1, then if the illumination 

 received when the earth's edge is at C, Fig. 1, were 

 represented by the ordinate C c, Fig. 2, the illumination 

 when the earth's edge reached K, L, M, Fig. 1 would 

 be represented by such ordinates as K^-, L Z, Mm. 

 Here O M would correspond to about 4'. Suppose, now, 

 another diagram made, as in Fig. 3, in which O M repre- 

 sents the M of Fig. 2, enlarged, and M m represents 

 the ordinate M m of Fig. 2, enlarged in much greater 

 degree. Then the earth's further progress as S M of 

 Fig. 1 is traversed, minute (of arc) after minute, carries 

 the edge to the points P, Q, R, Fig. 3. The illumination- 

 ordinates shorten now much more quickly than those in 

 Fig. 2. We get such a curve as mpq r, where Q 2 is 

 less than a fourth of M ^ii, but R r less than a tenth of 

 Q q (the real proportions are probably somewhere about 

 this). We see then that if s S s', Fig. 4, represent a part 

 of the edge of the geometrical shadow of the earth on 



Fig. 2. 



Fig. 3. 



Fig. 4. 



the moon, rUr' and q Q q' rings respectively 1' 

 2' from that shadow, the average illumination 

 the area q R q' is greater than that over the area i 

 somewhat as the area R r g Q in Fig. 3 is greater 

 the area R r. Now if Orqp m in Fig. 3 were a 

 bola, the area Kr q Q would be seven times O R r. 

 we have seen that in passing from M to we get 

 nates shortening far more rapidly the nearer we dr;: 

 0. Hence the illumination of q R q' exceeds the 

 mination of r S r' in far greater degree than tli 



prob.iblj ( i^ 

 estim it. ( f 

 edgt) It I, 



I ti.,.1 f, 



to d.n 

 appea 

 glare 

 furthi 



' to decel^ e 



i^tiuction based on a fair 

 f the sun s lustre near the 

 We cannot wonder, then, 

 t IS, regarding the eye as 

 {photometric aid, though 

 ) tin n ins-ition from light 

 11 ^Mtl lu the circle r K r' 

 / U / 111 cars light. The 

 uii)uu>5 surface helps still 

 _ , we learn fiom the sudden 

 change of aspect when that glare is gone, — the part 

 within s S «' which had seemed nearly black, appearing 

 thereafter (if refraction sends any light to it, as 

 ordinarily happens) to glow with a considerable amount 

 of ruddy lustre. 



Mr. Ranyard's remarks about refraction diminishing 

 the area of the shadow seem based on the mistake to 

 which I have already adverted, by which he has appa- 

 rently overlooked the exceeding narrowness of the 

 atmospheric zone which can refract the sun's light into 

 the shadowed region. If we could consider, as he seems 

 to do, the amount of refraction to indicate the degree to 

 which the shadow might be diminished, then indeed the 

 perplexities into which he seems to have involved him- 

 self might be under.stood. But as a matter of fact (or of 

 calculation, if that be preferred) refraction even though 

 effective to the very sea-level all round the earth's disc 

 as seen from the moon, cannot affect the shadow's size in 

 the slightest degree. The size of the shadow depends 

 on the position of the ring (see Fig. 4) at which the 

 degradation of light is so rapid that the eye recognises a 

 marked and sudden darkening; and this, as we have 

 seen, must occur somewhere outside the geometrical 

 shadow. (The question is rather physiological, though, 

 than physical.) Refraction can temper the darkness of 

 the umbra, but cannot in any way affect its size. All 

 over the umbra refraction is at work, usually with 

 tolerable uniformity, carrying a certain small proportion 

 of sunlight, variously coloured according to atmospheric 

 conditions, to illuminate the moon's surface. If one part 

 of this surface is illuminated by a longer arc, or by an 

 entire ring, than another, this other is illuminated by a 

 broader and brighter one. All parts get nearly the same 

 amount of light — at least, the absolute difference is 

 every where very small compared with even the difference 

 between the illumination along r R r', Fig. 4, and that 



• light 



along « S s' 

 So soon 

 moon, and only refi-action — e 

 refraction — can carry 

 necessarily a very feel 

 I showed (or rather es 

 light then received i; 

 fromourilluminatid : 



which the sun is .list. 

 earth, tli.' /...Tie ..f at,n, 



sea- level aiul of its ax 

 average brightness of t 

 ■fifth the average b. 



) direct light from the sun falls on the 



aof t 



L the most effective 

 have 



received from 



y. I take the 

 ight to be about 

 a r disc, and the 



also 



