298 Astronomy. [Lecture 19. 



there remains the angle O A L, equal to the angle 

 ALC, under which the earth's semidiameter AC 

 is seen from the moon. 



Now, since the sum of the angles of a plane 

 triangle makes two right angles, or 180 degrees, 

 and the sides of a triangle are always proportion- 

 ed to the sines of the opposite angles, say, as the 

 sine of the angle A L C at the moon L is to its 

 opposite side A C, the earth's semidiameter, or 

 8985 miles* so is radius the sine of 90 degrees, 

 or of the right angle A C L to its opposite side, 

 which is the moon's distance at L. from the ob- 

 server's place at A Or, so is the sine of the 

 angle C A L to its opposite side C L, which is 

 the moon's distance from the earth's centre, and 

 which will prove to be about 240,000 miles. 

 The angle C A L is equal to what the angle 

 O A L wants of 90 degrees. 



The sun's distance cannot so easily be deter- 

 mined, since his horizontal parallax, or the angle 

 O A S, equal to the angle A S C, is so small as 

 to be scarcely perceptible, being not more than 8 

 seconds and a half, whereas the moon's horizon- 

 tal parallax, or the angle O A L, is very discern- 

 ible, being at a mean 57' 18", which is more than 

 400 times greater than that of the sun. 



The sun's horizontal parallax, therefore, for 

 these reasons, could not be ascertained with 

 any degree of accuracy till the transits of Ve- 

 nus over the sun's disc, which happened in 

 the years 1761 and 1767, for at such an im- 



