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thefe in four fuccelTive lines below each other, and by their 

 fides their three fucceflive differences for each 12 hours; mul- 

 tiply each of thefe laft numbers by 5, taking the degrees for 

 minutes and the minutes for feconds, and you will have three 

 other numbers that will accurately denote the horary motions 

 at the mid-intervals of the pairs they refpedtively belong to. 

 The reafon of multiplying by 5, &c. is merely for brevity and 

 convenience in finding the y^ of the motion in A. R. for 12H. 

 for a X 60 -^ 12 = a X 5', which laft is much the moft conveni- 

 ently and readily done. 



Having thus got the horary motions for the mid-intervals of 

 6H, and 18H. to get ihem for any other hour and minute 

 you have only to take the difference of the horary motions at 

 the beginning and end of the period of 12HS. that includes the 

 hour and minute for which the rate is required, and fay, as 

 12H. is to the whole difference, fo is any other number of hours 

 and minutes to a proportionate part ; which added or fubtrad- 

 ed as occafion requires, to or from the rate of the neareft 

 mid-interval, gives the rate at the time demanded. Let it be 

 required, for example, to find the moon's horary motion in A. R. 

 for 6H. 30'. on the 5th Jan. 1789. 



Jan. 4, at 

 5, at 



5. at 



6, at 



H. 



30' 20" horary motion 4th day at 1 8 



31 20 horary motion 5th day at 6 



32 20 horary motion 5th day at 18 



Here 



