EC L 



3. The distance of the centres of the moon and of the earth's shadow, 

 when the moon's disk just touches the shadow (if d = moon's diameter) 



Cor. If P = 57'. 1", p 8", 8, and =: 16'. 1".3, we have the mean 



apparent | diameter of the earth's shadow =. 41'. 8".5, which is nearly 

 three apparent diameters of the moon. Hence since the moon in the 

 space of an hour moves over a space nearly equal to its diameter, the 

 moon may be entirely within the shadow, or a total eclipse may endure, 

 about two hours. 



4. The apparent | diameter of a section of the penumbra at the moon's 

 orbit 



And the distance of the moon's centre and of the centre of the shadow, 

 v/heu the moon first enters the penumbra, is 



5. To find the time, duration, and magnitude of a lunar eclipse. 

 Let m moon's motion in longitude, 



n moon's motion in latitude, 



s sun's (or the shadow's centre's) motion in longitude, 



X moon's latitude when in opposition, 



t time from opposition, 



c ~ distance of moon and earth's shadow, 



jind-let m ^ 8 = tan. 6. 



then t = 1 5 A sin. B -j- sin. 9 V (c I* cos. ^) 



5* 



