OF ECLIPSES OF THE SUN. 469 



With the centre S, and sum of the semidiameters of the 

 sun and moon, as a radius, describe arcs, cutting the apparent 

 orbit in B and E, which will be the moon's apparent places 

 at the times of beginning and end. From S. draw SG per- 

 pendicular to a straight line joining B and E; then G will 

 lie the moon's place at the time of greatest obscuration. And 

 tlu point in which LS, produced if necessary, cats tin- appa- 

 rent orbit, is the moon's place at the time of apparent eclip- 

 tic conjunction. Take the distance between the hour point 

 next preceding the point B, and that next following it: and 

 applying it to the scale, obtain its measure. Do the same 

 with the distance between B and the hour point next prece- 

 ding. Then, as the 1st distance : 2d distance : : 60 min- 

 utes : the time past the preceding hour at which the eclipse 

 begins. The other times are found in the same manner: and 

 the quantity of the eclipse is found in the usual manner. 



Find the moon's parallax in right ascension and declination 

 for the time of beginning, and make S; equal to the parallax 

 in declination. From z. draw zZ, parallel to FII. drawing 

 it to the right hand when the time is in the forenoon, but 

 to the left when it is in the afternoon, and make it equal to 

 the parallax in right ascension. Join SZ. which will repre- 

 sent a vertical circle passing through the sun's centre : and 

 the angle BSZ will be the angular distance from the sun's 

 vertex, of the point at which the eclipse commences. 



The slighl changes necessary in the construct ion. for places 

 near the equator or in the southern hemisphere, are so obvi- 

 ous as not to require notice. 



In finding the times of beginning, &c. tin- moon's motion 

 in the apparent orbit is assumed to be uniform during the 

 hour, which is no! strictly true. The greatest error, how- 

 ever, that can arise from the assumption, is only about a mi- 

 nute, when the latitude of the place is to . For higher 

 latitudes it will be less; and for places nearer the equator it 

 will be rather more. The error that may arise from assum- 

 ing the part of the apparent orbit, between two consecutive 

 hour points, to be a straighl line, will seldom be as great as 



