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WILCOCKS' REFLECTIONS ON THE 



Thus, if S be the solar system and A the focus 

 about which the star revolves, A B will represent 

 the radius of its orbit, and shall be equal to the 

 distance over which light travels in one unit of 

 time. 



A is at rest with respect to the solar system, and 

 all parts of the line H, A, B being nearly equidis- 

 tant from S, we may neglect altogether the time 

 occupied by light in passing from A to S. 



We will suppose that the ring makes a revolution 

 round the star in ten units of time, and in the same 

 period the star advances thirty degrees in its orbit. 

 The points B, C, D, E, F, G, H represent posi- 

 tions of the star at the moments when the opening 

 in the ring is in a line with the star and the earth. 

 Let us suppose the star at B ; it is visible, but the 

 revolution of the ring soon hides it from the in- 

 habitants of the earth, and the star and the ring 

 advance toward the position C. This being reached, 

 the opening in the ring is again in a line with the 

 star and the earth. 



It is manifest that in gaining the position C, the 



star has receded from the solar system, and is 



further than it was at B, by the distance Cc, the 



sine of B C, an arc of 30°. Its light must travel over Cc in addition to A S. The 



star is invisible, therefore, during a period consisting of the time of revolution of the 



ring, and that required by its light to travel over the sine of 30° of its orbit. 



The revolution of the ring requires 10. units, the journey of the light over the sine 

 of 30°, .500 The star will be hidden 10.500 



But in its progress from C to D, the star does not recede from the earth as much as 

 while passing from B to C, because the sine of 60° is not double that of 30°. 



The sine of 60° is .867 from which deduct the sine of 30° .500 and add 10. for the 

 revolution of the ring, and we have .867 — .500=. 367+10. =10.367 the period the 

 star will be invisible while passing from C to D. 



We obtain the next period by deducting sine 60° from the radius, and adding 10. 

 for the revolution of the ring. 1.— .867 = .133 + 10.= 10.133 



Thus while passing through the portion of its orbit between B and E, the star will 

 be hidden successively periods of 10.500 10.367 and 10.133 



To carry the star through the second quadrant of its orbit, we should, upon the 



