Nov. 28. 1884.] 



KNOWLEDGE ♦ 



445 



round the southern, the actual maximum (apart from 

 cloudiness of the air) being at the jioint marked M, on C S 

 produced. The north pole of the earth is at P, supposed to 

 be on the face of the earth turned moonwards at this 

 moment. This face is shown in Fig 2. 



Fig. 2. — Eartli's Fju-o tarneil Jlooiiwards at the time of Central 

 Eclipse. 



Fig. 1 shows how the earth's centre, C, is situated with 

 respect to the centre of the sun, S. Both figures are for 

 the centre of the moon's earthward face. For other parts 

 of that face we should of course get different relations. 

 An observer on the moon travelling northwards or south- 

 wards from the centre of the moon's earthward face* would 

 shift the earth's centre southwards or northwards as from 

 C towards « or n respectively ; and it is easily seen he 

 could raise it no farther than s or n, where C .< or C n 

 represents the semi-diameter of the moon's disc in the 

 above table, reduced by one-400th part (because as the 

 earth's centre is shifted the sun's centre is shifted by about 

 one-400th part as much, his distance exceeding the earth's 

 distance 400 times). Travelling eastwards or westwards 

 from the centre of the moon's earthward face, the earth's 

 centre would be thrown eastwards or westwards,! by 

 distances which cannot exceed IG' 10" represented by C w 

 and C e. Thus we can describe the circle s eniv with 

 radius 16' 10" to show the area within which the centre of 

 the earth's disc would lie at the time of central eclipse as 

 seen from different parts of the moon's earthward face. It 

 will be seen that the eclipse was absolutely central for a 

 point on the moon corresponding to the position of S on 

 the di.'^c .« (' n n: This was not far from the place of 

 Tycho, shown at t. A lunar observer on Plato M-ould have 

 had the centre of the earth sittiate nearly as at p — outside the 

 disc SiS^Sj — and therefore would have had an arc of sun- 

 light round a part only of the earth's disc. In any other 

 place on the moon we have only to set the place in its 

 proper quadrant of the moon, as indicated by the letters 

 .<, e, n, w. We miyht make a map of the moon within the 

 circle sen lo (as suggested by the rays from Tycho), the 



* Not the same as northwards or southwards relatively to the 

 celestial eqnator, — but nearly northwards or southwards relatively 

 to the ecliptic. 



t Not westwards for an easterly movement, and vice rersil, 

 because as we face the full moon the eastward side is on the left, 

 whereas as an observer on the moon faces the earth the eastward 

 side of her disc is towards the riffht. 



only difference from an ordinary map of the moon being 

 that our map would interchange east and west, or appear 

 as the usual map does when held opposite a looking-glass. 



In Fig. 1, E, and E^ are the positions of the earth's 

 centre at the time of first and last contact with the total 

 shadow, and are obtained by describing an arc round S as 

 centre with radius C M — Cs -t- C S to cut L N in E, and Ej ; 

 Eo and E^ are the positions of the earth's centre when total 

 eclipse was just beginning and just ending, and are obtained 

 liy describing an arc round S as centre with radius equal 

 to C M - Cs - C S, to cut L N in E, and E,. S„ S„, S„ and 

 Sj, are the points where E„ S„ E„ S (produced), E^^ S 

 (produced) and Ej S meet the edge of the sun's disc. Lines 

 from parallel to tljese four lines meet the circle repre- 

 senting the earth's disc in the points e^, e.., e.„ and e„ 

 corresponding to those parts of the edge of the disc which 

 give the part of the umbra (i) first seen on the moon's face, 

 (i ) j-ist completing totality by coming up to the moons 

 eage ; (iii) just ending totality by leaving the moon's edge, 

 and (iv) last seen on the moon's face.* The corresponding 

 points are marked on Fig. 2, and ahso on Fig. 3, which 

 represent the " sun-view of the earth " for the time of 

 central eclipse. Only, of course, it will be noticed that as 

 both these maps are for 10 h. 2 m. Greenwich mean time 

 (p.m.), the aspect for the four epochs ju.st dealt with will be 

 considerably different. The times for these are respec- 

 tively : — 



(i) 8h. 15-2 m.-) 



(iii IMi. 15-Sm.( „ . , ,. , X 



(iii) llh. 48-Sm. ( Greenwich mean time (p.m.), 



and (iv) 12 h. 472 m. ) 



and about Hi m. later for Greenwich solar time. It will 

 be easy for the student to make corresjionding projections 



Fig. 3. — Sun view of th- Ea ih at t.'ie time of central Ec 

 Ocr. 4, 10.2 p.m. (G.M.T.) 



ipse. 



from Fig. 3, in which the longitude and latitude lines have 

 been left in for his guidance. For (i) the point A in Fig. 3 

 must be brought on the central meridian PP' ; for (ii) the 

 point B ; for (iii) the point C ; and for (iv) the point D. 

 Corresponding changes may be made in Fig. 2 ; but, as a 

 matter of fact, there is no occasion to use both projections. 



* These radii, C M — C s + C S are deduced from the consideration 

 that the earth's disc (radius C JI) is just to touch the sun's disc 

 (radius C S) (i) externally (ii) internally, as seen from only one 

 ]ioint on the moon's surface, that point being on the edge of the 

 moon's disc (radius C s). 



