404 THE POPULAR SCIENCE MONTHLY. 



of doubtfulness is more than yi-j- of the whole, although it is no more 

 than the angle subtended by a single hair at a distance of nearly 800 

 feet. If we call the parallax 8.86", which is probably very near the 

 truth, the distance of the sun will come out 92,254,000 miles, while a 

 variation of ^ of a second either way will change it nearly half a 

 million of miles. 



When a surveyor has to find the distance of an inaccessible object, 

 he lays off a convenient base-line, and from its extremities observes 

 the directions of the object, considering himself very unfortunate if he 

 cannot get a base whose length is at least ^ of the distance to be meas- 

 ured. But the whole diameter of the earth is less than 1X ooo of the 

 distance of the sun, and the astronomer is in the predicament of a sur- 

 veyor who, having to measure the distance of an object ten miles off, 

 finds himself restricted to a base of less than five feet, and herein lies 

 the difficulty of the problem. 



Of course, it would be hopeless to attempt this problem by direct 

 observations, such as answer perfectly in the case of the moon, whose 

 distance is only thirty times the earth's diameter. In her case, obser- 

 vations taken from stations widely separated in latitude, like Berlin 

 and the Cape of Good Hope, or Washington and Santiago, determine 

 her parallax and distance with yery satisfactory precision ; but if ob- 

 servations of the same accuracy could be made upon the sun (which 

 is not the case, since its heat disturbs the adjustments of an instru- 

 ment), they would only show the parallax to be somewhere between 

 8" and 10", its distance between 126,000,000 and 82,000,000 miles. 



Astronomers, therefore, have been driven to employ indirect meth- 

 ods based on various principles : some on observations of the nearer 

 planets, some on calculations founded upon the irregularities the so- 

 called perturbations of lunar and planetary movements, and some 

 upon observations of the velocity of light. Indeed, before the Chris- 

 tian era, Aristarchus of Samos had devised a method so ingenious and 

 pretty in theory that it really deserved success, and would have at- 

 tained it were the necessary observations susceptible of sufficient ac- 

 curacy. Hipparchus also devised another founded on observations 

 of lunar eclipses, which also failed for much the same reasons as the 

 plan of Aristarchus. 



The idea of Aristarchus was to observe carefully the number of 

 hours between new moon and the first quarter, and also between the 

 quarter and the full. The first interval should be shorter than the 

 second, and the difference would determine how many times the dis- 

 tance of the sun from the earth exceeds that of the moon, as will 

 be clear from the accompanying figure. The moon reaches its quar- 

 ter, or appears as a half-moon, when it arrives at the point Q, where 

 the lines drawn from it to the sun and earth are perpendicular to each 

 other. Since the angle H E Q = E S Q, it will follow that H Q is the 

 same fraction of H E as Q E is of E S ; so that, if H Q can be found, 



