A HISTORY OF SCIENCE 



here. The extent of his mathematical knowledge, 

 however, is suggested by the fact that he computed 

 in great detail the number of grains of sand that would 

 be required to cover the sphere of the sun's orbit, 

 making certain hypothetical assumptions as to the 

 size of the earth and the distance of the sun for the 

 purposes of argument. Mathematicians find his com- 

 putation peculiarly interesting because it evidences 

 a crude conception of the idea of logarithms. From 

 our present stand -point, the paper in which this calcu- 

 lation is contained has considerable interest because 

 of its assumptions as to celestial mechanics. Thus 

 Archimedes starts out with the preliminary assump- 

 tion that the circumference of the earth is less than 

 three million stadia. It must be understood that this 

 assumption is purely for the sake of argument. Ar- 

 chimedes expressly states that he takes this number 

 because it is "ten times as large as the earth has 

 been supposed to be by certain investigators." Here, 

 perhaps, the reference is to Eratosthenes, whose meas- 

 urement of the earth we shall have occasion to re- 

 vert to in a moment. Continuing, Archimedes as- 

 serts that the sun is larger than the earth, and the 

 earth larger than the moon. In this assumption, he 

 says, he is following the opinion of the majority of 

 astronomers. In the third place, Archimedes assumes 

 that the diameter of the sun is not more than thirty 

 times greater than that of the moon. Here he is prob- 

 ably basing his argument upon another set of measure- 

 ments of Aristarchus, to which, also, we shall presently 

 refer more at length. In reality, his assumption is very- 

 far from the truth, since the actual diameter of the 



210 



