338 GREEK SCIENCE. 



to be perceived by a thin stream of light on each side of the cylinder. 

 Now, if the eye perceived the sun from a single point, it would 

 suffice to draw from that point tangential lines to the two sides of the 

 cylinder. The angle included between these lines would be a little 

 less than the apparent diameter of the sun ; because there is a ray of 

 light on each side. But as our eyes are not a single point, I have 

 taken another round body, not less than the interval between the two 

 pupils ; and placing this body at the point of sight at the end of the 

 ruler, and drawing tangents to the two bodies, of which one is 

 cylindric, I obtained the angle subtended by the suns (apparent) 

 diameter. Now the body, which is not less than the preceding dis- 

 tance (between the pupils), I determine thus: I take two equal 

 cylinders, one white, the other black, and place them before me ; the 

 white further off, the other near, so near indeed as to touch my face. 

 If these two cylinders are less than the distance between the eyes, the 

 nearer cylinder will not entirely cover the one that is more remote, 

 and there will appear on both sides some white part of that remote 

 cylinder. By different trials, we may find cylinders of such magnitude, 

 that the one shall completely conceal the other : we then have the 

 measure of our view (the distance between the pupils), and an angle, 

 which is not smaller than that in which the sun appears. Now, 

 having applied these angles successively to a quarter of a circle, I have 

 found that one of them has less than its 164th part, and the other 

 greater than its 200th part. It is therefore evident, that the angle 

 which includes the sun, and has its summit at our eye, is greater than 

 the 164th part of a right angle, and less than the 200th part of a 

 right angle." 



By this process, Archimedes found the sun's apparent diameter to 

 be between 27' and 32' 56". 



singular It is not a little remarkable, considering the obvious inaccuracy of 



S^TraSt!* the method, that the maximum limit thus obtained, differs only ^ of a 

 minute from 32' 35'6", which is the largest angle actually subtended 

 by the sun's diameter, and which is observed about the time of the 

 winter solstice, when the sun is nearest to the earth. But this quo- 

 tation from the ' Arenarius ' is extremely curious also on other accounts. 

 We may learn from it, first, that Archimedes, with all his fecundity 

 of genius, and with all the variety of his inventions, had no means of 

 diminishing the effect of the sun's rays upon his eyes, and therefore 

 performed this interesting experiment when the sun was in the horizon, 

 that the optic organ might sustain its light without inconvenience. It 

 also proves to us, that there was not then any instrument known to 

 Archimedes, which he thought capable of giving the diameter of the 

 sun, to within four or six minutes; since he found it necessary to 

 devise means at which he stopped, after an attempt not very satis- 

 factory. We see, further, that he carried his angles, or their chords, 

 over a quarter of a circle ; but he does not say expressly that his arc 

 had been divided; to render his language accurately, it is simply 



