ALEXANDRIAN OR HELLENISTIC PERIOD 



sun is "more than 5832 times, and less than 8000" 

 times larger than the moon; though his measure- 

 ments, taken by themselves, give no clew to the 

 actual bulk of either body. These conclusions, be 

 it understood, are absolutely valid inferences nay, 

 demonstrations from the measurements involved, 

 provided only that these measurements have been 

 correct. Unfortunately, the angle of the triangle 

 we have just seen measured is exceedingly difficult to 

 determine with accuracy, while at the same time, as a 

 moment's reflection will show, it is so large an angle 

 that a very slight deviation from the truth will greatly 

 affect the distance at which its line joins the other side 

 of the triangle. Then again, it is virtually impossible 

 to tell the precise moment when the moon is at half, as 

 the line it gives is not so sharp that we can fix it with 

 absolute accuracy. There is, moreover, another ele- 

 ment of error due to the refraction of light by the 

 earth's atmosphere. The experiment was probably 

 made when the sun was near the horizon, at which time, 

 as we now know, but as Aristarchus probably did not 

 suspect, the apparent displacement of the sun's posi- 

 tion is considerable; and this displacement, it will be 

 observed, is in the direction to lessen the angle in 

 question. 



In point of fact, Aristarchus estimated the angle at 

 eighty-seven degrees. Had his instrument been more 

 precise, and had he been able to take account of all the 

 elements of error, he would have found it eighty-seven 

 degrees and fifty - two minutes. The difference of 

 measurement seems slight ; but it sufficed to make the 

 computations differ absurdly from the truth. The 



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