472 



KNOWLEDGE • 



[June 5, 1885. 



atmosphere (or rather towards that ring of atmosphere 

 operative in retracting the rays towards the moon) would 

 of course be convergent after passing through the atmo- 

 sphere. This distinction between the rays forming a 

 pencil of light, and the axes of different light-pencils, is 

 commonly a stumbling-block with optical students ; and 

 I think Herschel would have done well to remember this, 

 and to explain (however obvious the matter may be to the 

 more advanced) that he is not dealing with pencils of 

 light, nor therefore considering foci, in Arts. 421, ej si'q. 



The axes of light-pencils proceeding from any point on 

 the sun's face, would be deflected by the varying refractive 

 effects of the successive strata of the earth's atmosphere 

 (from the outskirts | roducing scai-cely any deflection to the 

 lowest layers, the rays actually grazing the earth's surface 

 being most deflected) into a region such as Herschel has 

 indicated in his treatment of the subject, before he limits 

 his remarks to grazing deflection only. Au eye situated 

 anywhere within this region would receive that particular 

 pencil which came in the i-ight direction to full on the eye- 

 pupil, instead of the pencil which the eye would have 

 received if the earth with its atmosphere were not in the 

 way ; and this eye, instead of seeing that point in its true 

 direction would see it as a point (or as nearly point-like as 

 a i-efracted pencil can make a point of light appear) appa- 

 rently close to the earth's glob?. This starlike point would 

 lie somewhere within two miles from the earth's surface, 

 which at the moon's distance would look like actual contact. 

 Or it might be, according to the position of the point, that 

 two pencils would be received by it, from opposite sides of 

 the earth. And, if we cau imagine such a thing as an 

 actual point of light being exactly beyond the earth's centre, 

 then the eye would receive pencils from all round the 

 earth, and that point of light would be transformed into an 

 exceedingly delicate ring. As the point passed the earth's 

 centre, its appearance would be changed from two starlike 

 images into this fine ring, and then instantaneously into 

 two starlike images again. 



With regard to the amount of light received from the 

 sun during a total lunar eclipse, Herschel and Mr. Mattieu 

 Williams are indeed at one in saying that all this light 

 comes from a ring of air, looking (as seen from the moon) 

 very small compared with the disc of the earth. And Mr. 

 Williams is quite right in his estimate of the apparent 

 size of that ring. In fact, he could not well have been 

 otherwise. Where he goes wrong is in supposing that 

 that ring would look no brighter than the sun-lit earth or 

 atmosphere, whereas it would really look as bright as the 

 sun's disc seen through just so much air as happened to 

 be along the track of the light-pencils received by our 

 imaginary eye at the moon's surface. Herschel very 

 rightly says that the illumination of the region from which 

 the ring-shaped image of the sun could be seen would be 

 very feeble. I have calculated what that illumination 

 would be if the absorption of light by the particular regions 

 of air operative in deflecting the sun's rays were about one- 

 half, and I find that the amount of light would be only 

 -pfL__th of full .sunlight. This would be the maximum, 

 and even this we could hardly admit if we did not 

 remember that the rays actually received on the moon's 

 surface during mid-totality are not for the most part 

 refracted through the lowest parts of our air, but through 

 regions a mile or two above the earth's surface, where the 

 absorption is very much less than what we recognise in the 

 case of the setting sun. 



But Mr. Williams, anxious to show that I differ from 

 Herschel, who had also said that the light would be feeble 

 compared with sunlight, considers that I have no right, by 

 my own showing, to agree with Kerschel. " Mr. Proctor 



surely understands that if the irhoh sun is represented by 

 that ring, in the manner he describes, the intensity of the 

 luminosity of the ring, as compared with that of the solar 

 disc, will vary inversely with the apparent area of the ring 

 as compared with the apparent area of the disc ; or, other- 

 wise stated, the total luminosity of the ring will be equal 

 to the total luminosity of the disc (viewed under like cir- 

 cumstances) whatever be their comparative areas." But 

 this is what I not only do not " surely understand," but 

 deny and reject utterly. I have shown (Kxowledge, Vol. 

 IV., pp. 133-34) that no optical contrivance whatever can 

 make an object look brighter than it really is ; apart from 

 absorption which diminishes light, we get exactly the same 

 brightness, neither more nor less, whether an object be 

 magnified or parvified (if I may be allowed to coin a word), 

 so only that it be not magnified so much that the pencils of 

 light from individual points do not fill the whole eye-pupil.* 

 Short of this degree of magnification, we get more light 

 from an object, the larger it is made to look, by any con- 

 trivance of lenses or reflectors, but its apparent intrinsic 

 lustre is not changed, except by absorption of light ; and 

 the smaller an oliject is made to look by parvification, the 

 less light we get from ir. Now, the earth's atmosphere 

 does not act differently in this respect from optical con- 

 trivances made by man. It reduces the sun's image in size, 

 besides very curiously affecting his apparent shape ; but it 

 cannot alter his apparent lustre, except by reducing it 

 through absorption. Thus the light from that ring-shaped 

 image of the sun is less than the light from the sun itself, 

 in the same degree that that image is less than the solar 

 disc, and also in proportion as the sun's light is absorbed. 



Mr. Williams may probably say that I have here simply 

 repeated what he holds to be an incorrect statement. But 

 I cannot do much more. The general proof of the law 

 that under no circumstance can the apparent brightness of 

 a luminous surface be increased cannot be understood with- 

 out more special study of the laws of brightness than Mr. 

 Williams has yet cared to make. I have given the proof 

 in the Monthly Notices of the Astronomical Societij, and no 

 one acquainted with the laws of optics will for a moment dis- 

 pute the matter. In point of fact, any optical contrivance 

 or natural arrangement of refracting media or reflecting 

 surfaces by which a body is made to look smaller, produces 

 effects equivalent to those resulting from increase of 

 distance, and we no more get full sunlight from a diminished 

 image of the sun than we get full sunlight from some star 

 which, though as large as our sun, is reduced to a much 

 smaller apparent size by its much greater distance. In 

 whatever degree the sun's apparent size, as supposed to be 

 seen from the moon, is reduced by the interposition of the 

 earth, in that degree at least is the amount of light falling 

 on any part of the moon reduced. If Mr. Williams will 

 look at the sun through an opera-glass turned small end 

 from him, or at the small image of the sun seen in a convex 

 reflecting surface of small radius, he will have at any rate 

 two good examples of the general law I have indicated. 



I might, in conclusion, notice — but I am not sure the 

 force of the illustration will be felt — that the same con- 

 siderations which lead to the mistake that a starlike point 

 beyond the earth's centre would not be visible from the 

 moon's surface, would show also that a star would not in 

 general be visible when near the horizon. For if we take 

 any particular layer, say the lowest, of our air, it is certain 



* For instance, when we use a high power on a planet or on the 

 moon, the beams of light sent by the object-glass to a focus (the 

 image of a point on the observed body) are intercepted by the eye- 

 piece before they have opened out to the breadth of the eye-pupil ; 

 the higher the power, the narrower are these emergent beams, and 

 tlie fainter is the illumination (^f the object. 



