BoEDDiCKER — On Idiuar Radiant Heat. 503 



II. — Construction of a Curve representing approximately the Change of the MoorHs 



Light during the Eclipse. 



1. A short discussion of the heat-curve just obtained is more conveniently 

 deferred till after the means have been supplied to compare it with a curve 

 representing the variations of the lunar light during the eclipse. The dates for 

 the computation of this curve were obtained as follows : — 



The usual formulae (Appendix to Nautical Almanac for 1836) furnished for 

 the eclipse: — 



Semi-diameter of shadow, ...... 2558"8" 



Semi-diameter of penumbra, 4511*8 



Depth of penumbra, 1953"0 



Diameter of Moon, 1905-8 



Semi-diameter of Earth (as seen from the Moon), . . 3490-1 

 Semi-diameter of Sun (as seen from the Moon), . . 971*7 



I now assumed the depth of the penumbra to be equal to 80 x 24-4" = 1952, 

 and for the diameter of the Moon 



78 X 24*4" = 1903-2", 



and divided the penumbra by concentric circles into 80 zones, so that the 

 difference between the semi-diameters of two successive zones was 



R"> - i2"'« = 24-4, m = 0, 1, 2 ... 80 and 



jB° = 4511*8 = radius of penumbra, 



i?'" = 2559*8 = assumed radius of shadow. 



The Moon was now supposed to move uniformly along a semi-diameter of the 

 shadow, and the arese successively cut off by the concentric circles computed by 



the formula 



^»"' = {4>,r - h sin 2<^„») p' + ie-^ sin 2^/') R'^'' 



m = 0, 1, 2 ... 78 



m = 0, I, 2 . . . 80 



where p = 951*6 = the assumed radius of the Moon, and consequently ^ = 24*4. 



The angles ^ and 6 were obtained from 



An"" + p'-R"'^ J ^ p sin <^„'" . . „ 



2A% =''''^" ' ^-^ = «^^^"'"- 



39 -w 

 39 

 the distance between the centre of the penumbra and the centre of the Moon. 



Here is A„'" = R'" + -g^- p 



