DISTANCE AND GRANDEUR OF THE SUN 87 



Moreover, it was difficult then to get a long base for observa- 

 tions, such as their crude measures of angles required. So, 

 beginning with the moon, they resorted to the ingenious plan 

 of taking its parallax when it lay in the horizon of one point 

 of observation. Obviously at this moment the direction of 

 the moon was at right angles to a plumb-line at that point, 

 and hence to the centre of the earth, as a glance will show : 



FIG. 7. 



It is clear that if a second point on the earth, as D, can be 

 found where the moon is at the same moment directly on the 

 meridian, then a line from the moon through this point will 

 equally pass through the earth's centre. As a matter of fact, 

 it would be rather painful work to locate this point, but it can 

 be reckoned, and we have again a right-angled triangle in which 

 the distance of the moon is given in terms of the earth's radius, 

 C H. Ptolemy, in his treatise, describes another simple method, 

 and there were doubtless others still. They did not agree very 

 closely ; the distance is, in reality, a troublesome quantity 

 to compute, because it varies. Its least and greatest distances 

 were fixed at from 50 to 85 earth's radii, so that, taking 70 

 as a mean, they were not far out. And with the circumference 

 of the earth fixed, they knew that the moon was somewhere 

 around 240,000 miles from the earth. 



They could likewise note that its apparent or visual diameter 

 is half-a-minute, and, the distance known, could compute that 

 this mild-mannered orb was in reality a colossal thing a body 

 some 2000 miles through, that is, a quarter of the diameter 

 of our massy earth. 



The temperature of the calculating spirit is proverbially 

 low ; but if the hand of Newton could so tremble with excite- 

 ment as he foresaw that his figures would demonstrate the 

 great law he had divined, with what profound amazement must 

 he who first computed the moon's magnitude have laid down 

 his pen ! This softly glowing disk, whose apparent size is so 



