6 RROWN : 



The actual diameter of the sun in miles can be computed. 



The value of each of the chords spoken of above can be 

 ascertained by the time occupied in describing it — since the 

 motions of Venus and those of the sun are known from the 

 tables. The sun's angular semi-diameter is 15' 51" (nearly). 

 Venus in 1769 opened an angle on the sun's disc of 4' per 

 hour or 4" per minute. At this rate Venus would have occu- 

 pied a certain time in describing the known angular diameter 

 of the sun. The times occupied in describing the two chords 

 would when brought together and compared give their ratio to 

 diameter. And thus their values and those of the arcs they 

 intercepted would become known. For example : The sun's 

 angular semi-diameter being 15' 51" the planet in her transit 

 would have occupied 3 hours, 57 min., 45 sec. in opening that 

 angle. If now she had occupied exactly that time in describ- 

 ing the chord observed from either station the observer would 

 have known at once that the chord was equal to the sun.'s 

 semi-diameter and hence the arc equal to 60°. Each chord is 

 double the sine of half the arc that it intercepts. Therefore 

 the sine of half the arc, and of course the versed sine, becomes 

 known ; and the difference of the two versed sines is the 

 breadth of the zone in question. The versed sine of one arc 

 is a certain fractional part of radius ; the versed sine of the 

 other arc is another fractional part of radius. Their differ- 

 ence, which is known to be 17,640 miles, is a certain frac- 

 tional part of radius. Thus the sun's radius, and of course 

 also his diameter, becomes known. It is 882,000 miles. This 

 gives the real length of the chord described on the sun In^ 

 Venus and the real length of their difference. Now compute 

 by Rule of Three what must be the distance at which 882,000 

 miles will subtend a given angle — in other words, of what 

 number is 882,000 the io8th part. The number is 95,256,000, 

 and thus another and a reasonably accurate inference can be 

 drawn as to the sun's distance from the earth. 



But the sun's semi-diameter was known at the time in 

 question l)y angular measurement only, and not with sufficient 



