504 BoEDDiCKER — 0)1 Lunar Radiant Heat. 



Thus we obviously have A^^ = 0, or external contact, and A-^° = 951 -6^ tt, or 

 internal contact between moon and penumbra. Equally R}, B? . . . B^" will 

 respectively cut off the arese : — 



Ao' (=0),A,\A,' .. ..A,s'i=95V6"-7r). 



vl„- (= 0), A,\ A,' A,,' {= 95l-6^-7r), etc. 



Ao" (= 0), Ar, A.'' . . . A,,"> (= 951-6^-7r). 



These arese were rigorously computed for m — 0, 10, 20, . . . 60, 70, 80, and, of 

 course, w = 0, 1, 2 . . . 77, 78 for each «?, and the intermediate values interpolated. 

 The portions of the Moon, lying successively in one special zone m, enclosed by 

 the two concentric circles described with K"'~^ and R'" will then obviously be 



^i'"-', A^'"-^ - Ai", A3""' - A{\ etc. till A.,i"-' - A„'" 



where now to = 1, 2, 3 . . . 80. 



2. I next computed the uneclipsed arese of the Sun (as seen from the Moon) for 

 80 points of equal distance, thus obtaining 82 values A^*, Ai*, A^* . . . A^*, A^i*, 

 of which Ao* = 100 denotes the full, and ^si* = the totally eclipsed Sun as seen 

 from the Moon during the progress of the eclipse. These quantities, which 

 represent approximately the luminosity of the successive penumbral zones — if we 

 neglect the decrease of the Sun's light towards its limb — were plotted down in a 

 curve, and the numbers corresponding to the middle point of each zone read off. 

 These values 



Fo (= 100), F„ F„... Fso, Fs, (= 0) 



are the light-factors, with which the portions of the Moon which lie in the 

 corresponding zones of the penumbra have to be multiplied in order to represent 

 the Moon's luminosity during the progress of the eclipse. At any particular 

 moment — that, for instance, of internal contact between Moon and penumbra, the 

 Moon's luminosity will then be expressed by 



A,,' F, + {A,,' - An') F, + (A:,' - A„') F, + . . . 



+ {A"\:, . ,„, -A""\,,. ,„ , 1)) Z,„ + . . . + (^2" - ^s^^) ^77 + 4i'^ ^78. 



Thus 159 quantities were deduced which represent, with considerable approxi- 

 mation, the changes of the Moon's light during the progress of the eclipse, i. e. 

 during the Moon's motion through the penumbra into the shadow. 



