140 OUTLINES OF NATURAL PHILOSOPHY. 



144. Considering the small arches moved o- 

 ver by the moon, and the section of the shadow, 

 during the time of an eclipse, as straight lines 

 given in position, and described by two points, 

 viz . the centre of the moon's disk, aud the cen- 

 tre of the section of the shadow, moving with 

 given velocities, the determination of the phe- 

 nomena of a lunar eclipse is reduced to the so- 

 lution of a geometrical problem. 



Let ST and MP, (fig. 14.), represent the portions of 

 IK;: the ecliptic, and of the moon's orbit traversed, du- 

 ring the time of a lunar eclipse, the first by the 

 centre of the section of the shadow, and the second 

 by the centre of the moon, considered as straight 

 lines. Let S be the centre of the earth's shadow, 

 and M the centre of the moon at the instant of the 

 opposition, and let S' and M' be any other cotem- 

 porary positions of these centres ; SS' and MM' 

 being taken in opposite directions. Draw S'N pa- 

 rallel to SM ; and join M'N. Let t be the time 

 in which SS' and MM' have been moved over, 

 reckoned from the moment of the opposition, in 

 hours and decimals of an hour ; let the horary 

 motion of the moon in longitude be m, so that 

 MO = m t ; her horary motion in latitude A, so 

 that M'O = A t ; and let the horary motion of the 

 sun or of the shadow be n, then SS' = MN = n t. 



Also 



