DISTANCE ORBIT MAGNITUDE. 



and it will apparently diminish in size as its distance is increased. 

 Let it be removed until it becomes equal in apparent magnitude to 

 the moon, so that it will exactly cover the moon, and neither more 

 nor less. If its distance be then measured, it will be found to be 

 about 120 inches, or 240 half inches. But it is known that the 

 distance of the moon is about 240000 miles, and consequently it 

 follows in this case, that 1000 miles in the moon's distance is 

 exactly what half an inch is in the coin's distance. Now under 

 the circumstances here supposed, the coin and the moon are 

 similar objects of equal apparent magnitude. In fact the coin is 

 another moon on a smaller scale, and we may use the coin to 

 measure the moon's distance, provided we know the scale, exactly 

 as we use the space upon a map of any known scale to measure a 

 country. But it has been just stated that the scale is in this case 

 half an inch to 1000 miles ; since, then, the coin measures two 

 half inches in diameter, the moon must measure 2000 miles in 

 diameter. The moon is then a globe whose diameter is about one- 

 fourth of that of the earth. 



This may be rendered still more clear by reference to the 

 annexed diagram (fig. 1), where E is the eye, c the coin, and M the 

 moon. It will be evident on mere inspection, that the triangle 

 formed by the distance EC of the coin from the eye, and the 

 diameter cc of the coin, is similar to the triangle formed by the 

 distance EM of the moon from the eye and the diameter aim of the 

 moon, and that consequently the proportion of EC to cc is exactly 

 the same as that of EM to x;. But as has just been stated, it is 

 found that when cc exactly covers the moon, and neither more nor 

 less than covers it, EC is 120 times cc. It follows, therefore, that 

 EM is 120 time* iim. But since it has been ascertained that EH is 

 240000 miles, that is 120 times 2000 miles, it follows that MW is 



2000 miles. 



Fig. 1. 



5. While the moon moves around the earth, we find by observa- 

 tions of its appearance, that the same hemisphere is always turned 

 toward us. We recognise this fact by observing that the same 

 marks always remain in the same place upon it. Now, in order 

 that a globe which revolves around a centre should turn continu- 

 ally the same hemisphere toward that centre, it is necessary that 



D2 35 



