April 24, 1885.] 



♦ KNOWLEDGE ♦ 



341 



in the form of a line h S' on the earth's edge. The part 

 B A would be seen on both sides of the earth. 



As this holds for every diameter of the sun's face, it 

 follows that the ring seen round the sun would be a very 

 singularly distorted image of the sun ; one may say there 

 would be two images of the sun. Out.<;ide the circle into 

 which the point C would be transformed, a circle very close 

 to the earth's edge, there would be an image of the sun in 

 the form of a rinsr, such as would be jiroduced if a bright 

 circle were dixided into an infinite number of sectors, and 

 each were carried a considerable distance (the same for 

 each) radially from the centre, all of them shortening 

 equally as they retreated, and also widening so as to form 

 a complete ring. Inside the circle into which would be 

 transformed, there would bo another circular image of the 

 part of the sun inside the dotted circle A B D E, a ring 

 image svich as would be produced if a bright circle were 

 divided into an infinite number of sectors, and each were 

 carried a considerable distance (the same for each) radially 

 across and then from the centre, so that they would go to 

 the opposite sides from that which they had before occu- 

 pied, shortening and widening as they went, so as to form 

 a complete ring. 



Fig. 3. — IIlnBtrating the digtortion of the sun's face, around the 

 disc of the earth, as supposed to be observed at the time of central 

 total lunar eclipse from the moon. 



An idea of the actual distortion of the solar diac in this 

 way (in the case where the eclipse is central and the whole 

 breadth of the sun is supposed to be just lifted into view all 

 round) may be conveniently obtained from Fig. .'!. Here 

 A B E D ia supposed to represent the sun's disc, A B, D E 

 the spot zone.", P Q the outline of the earth's disc ; and the 

 ring-shaped double image of the sun formed around the 

 earth is supposed to be enormously exaggerated in width, 

 so as to form the double ring ah ed a I' e' dJ, c c' represent- 

 ine the circle into which the centre C of the sun's face is 

 altered. If we imagine the double-ring image compressed 

 into the form of a very narrow ring of uniform width, the 

 true nature of the distortion of the solar image would be 

 represented. The row of large spots A B (purely 

 imaginary, of course) is altered into the arc a i on the outer 

 part of the rin?, and into the arc a' V on the inner part, 

 while the row D E is altered into the arc d e on the outer 

 half and into the arc d' e' on the inner half. 



The di^fortion where the eclipse is not central is ditlerent. 

 In such a case as i.s illustratrd in Fig. 2, there is a cnmplete 

 image of tlie sun as at k s //*•' (the points thus n-.arked cor- 

 responding to the points KS K'S' of the solar disc) on one 

 side of the earth ; while on the opposite side there is an 

 image I s' I' b of the portion L S' L' B' of the sun's face. Of 

 course the breadth of these distorted images is considerably 

 exaggerated. 



The student will find it a useful exercise to indicate the 

 distortions corresponding to other cases, as when the 

 central point C falls within S K K' but not centrally, at C. 

 So the case corresponding to the transit of Venus or 

 Mercury, where the disc of the ])lanet is small compared 

 with that of the sun, will be found interesting to deal with. 

 Hereafter I may consider transits of Venus and Mercury 

 in a separate paper. 



It remains only to consider how much light may reach 

 the moon in this way during central totality. 



Taking il miles as the probable extreme height of the 

 parts of the atmosphere effective in lifting the sun into 

 view (that is, supposing a s, b s, in Fig. 1 severally equal 

 to 21 miles) and further supposing the air as clear as 

 possible, and free from cloud or dust, we may perhaps 

 assume the intensity of sunlight reduced no more than 

 one-half by atmospheric absorption. By this I mean that 

 the average absorption for the ring s es' <Z (Fig. 1) is one- 

 half. In this case, we should get the maximum amount 

 of illumination. We have only to compare, then, the ap- 

 parent area of the ring sds'd' -with the apparent area of 

 the sun, and to take this absorption into account to be 

 able at once to determine how much light the moon can 

 receive at a point on her surface where the eclipse ia 

 absolutely central. At other jioints of course she will 

 (under similar conditions) receive more light. 



Now remembering that C« (Fig. 1) represents 57', and 

 CS 16', we have, since «s = 2.',-^3960 C a. 



ring s e s' d' : disc S S' : : 2 jr 57 < 



(16)- 



2x3960 

 : : 285 : 3960 x 2.")6 

 or light from 



s « s' d! : full sunlight : : 570 : 3960 x 256 



: : 57 : 399 x 254 approximately. 

 ■ '■ - :: 1 : 1778 



Supposing the air so far wanting in clearness that the 

 average brightness of s e s' d' was but the twentieth of sun- 

 light, the minimum illumination of the moon's disc would 

 be still onel7, 780th of sunlight illumination. Now if the 

 earth's albedo or light- reflecting power is about the same as 

 the moon's, which may fairly be assumed, then her light 

 when full in the moon's skies, as when she is illuminating 

 that part of the new moon which is sometimes called " the 

 old moon in the new moon's arms," is about one-46,000th 

 part of sunlight, or less than one- third the light illuminating 

 the moon's surface during total eclipse if the earth's air 

 absorbs nineteen-twentieths of the sun's light, and less than 

 one thirtieth of that light if the air absorbs (on the 

 average) one half of the sun's light. It must be remem- 

 bered too that we have comparatively imperfect means of 

 measuring the amount of light coming from the earth- 

 illuminated parts of the new moon, the contrast with the 

 sun-illuminated part being so great. During partial lunar 

 eclipse the earth's shadow looks very much darker than 

 when totality has bfgun, and the contrast with the un- 

 eclipsed parts no longer deceives the eye. 



Of course, if there are cloud banks round any part of the 

 circumference adhe. Fig. 1, the illumination of the ring 

 s e ,s' d is correspondingly reduced, — as indeed the area of 

 this ring is reduced. If there were conceivably clouds 



