ECLIPSES. 



diameters, and either total or partial interposition must take 

 place, according to the relative magnitudes of their discs, and to 

 the distance between the points of their respective paths at which 

 their centres are simultaneously found. 



10. This will be easilywendered intelligible. Let A, fig. 1, be 

 the disc of the object eclipsed, and a be that of the interposing 

 object which eclipses it. So long as the distance between the 

 centres of the two discs is greater than the sum of their semi- 

 diameters, it is evident that the one disc will lie altogether out- 

 side the other, so as not to intercept the view of any part of it, 

 This will be apparent from an inspection of fig. 1. 



1 1 . This may be briefly explained thus : If E be the semi- 

 diameter of A, and r that of a, and D be the distance between the 

 two centres, then the one disc will lie altogether outside the other 

 so long as D is greater than n -f r. 



Fig 1. Fig. 2. 



' 



12. If the distance between the centres be equal to the sum of 

 the two semi-diameters, then the two discs will touch each other, 

 without either actually intercepting a part of the other. This 

 case is shown in fig. 2, and is briefly explained thus: If 

 D = R + r, the two discs will touch without encroaching one 

 upon the other. This position of the discs is called external 

 contact. 



13. If the distance between the centres of the two discs be less 

 than the sum of the two semi- diameters, then one of the discs 

 will necessarily encroach upon the other and a partial eclipse will 

 take place. This case, is shown in fig. 3. The breadth of the 



Fig. 3. Fig. 4. 



part of the disc A obscured by a is evidently equal to the 

 difference between the sum of the semi-diameters of the two discs 

 and the distance between their centres, which is briefly expressed 

 thus : If E, + r be greater than D, then the one disc will encroach 

 upon the other, and the breadth of the part intercepted will be 



E + r D. 

 14. If the distance between the centres of the two discs be 



364 



