ITS VELOCITY. 



discovery of Jupiter's satellites, Roemer, an eminent Danish 

 astronomer, engaged in a series of observations, the object of 

 which was the discovery of the exact time of the revolution of 

 one of these bodies around Jupiter. The 

 mode in which he proposed to investigate 

 this, was by observing the successive 

 eclipses of the satellite, and noticing the 

 time between them. 



Let s (fig. 1) represent the sun, and A B 

 c D E F G H the successive relative positions 

 of the earth. Let j be Jupiter projecting 

 behind him his conical shadow, and let M 

 is represent the orbit of one of his satel- 

 lites. After each revolution the satellite 

 will enter the shadow at M, and emerge 

 from it at N. 



Now if it were possible to observe 

 accurately the moment at which the satel- 

 lite would, after each revolution, either 

 enter the shadow, or emerge from it, the 

 interval of time between these events 

 would enable us to calculate exactly the 

 velocity and motion of the satellite. But 

 by attentively watching the satellite we 

 can note the time it enters the shadow, 

 for at that moment it is deprived of the 

 sun's light, and becomes invisible. We 

 can also note the moment of its emer- 

 gence, because then escaping from the 

 edge of the shadow, it comes into the sun's 

 light, and becomes visible. It was in this 

 manner that Roemer proposed to ascertain 

 the motion of the satellite. But in order 

 to obtain the estimate with the greatest 

 possible precision, he proposed to continue 

 his observations for several months. 



Let us, then, suppose that we have 

 observed the time which has elapsed 

 between two successive eclipses, and that 

 this time is, for example, forty-three hours. We ought to expect 

 that the eclipse would recur after the lapse of every successive 

 period of forty-three hours. 



Imagine a table to be computed in which we shall calculate 

 and register beforehand the moment at which every successive 

 eclipse of the satellite for twelve months to come shall occur, we 



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