OPTICS. 355 



If the eye advance, distant objects will appear to be left behind. 

 If an object appear to augment, we judge that it is approaching 

 towards the eye. 



Objects unequally distant, which are not in a right line, may some- 

 times give the idea of a concave surface, and, at others, the idea of a 

 convex surface. 



These propositions relate to direct vision : there are a few which 

 relate to reflection. Among these we find the problem, to find the Problem, 

 height of an object by its shadow, or, in the absence of the sun, by 

 means of a mirror, on the principle of the equality of the angles of 

 incidence and reflection. 



Euclid also attempts to determine the burning point of a concave 

 spherical mirror, but errs in his conclusion ; for he supposes that this 

 point is the centre of the concavity, or the centre of the sphere. 



How long this error in theoretical deduction remained unconnected, 

 it is not easy to say : it is well known that the ancients employed 

 concave mirrors to rekindle the vestal fires. Plutarch, in his ' Life of 

 Numa,' gives a description, not very distinct, however, of the cxce^tta, Numa. 

 or dishes, which they thus employed. They seem to have been con- B - c - 71 - 

 cave polished hemispheres, or segments nearly hemispherical; and A.C. 98. 

 Plutarch tells us, that the combustible matter was placed in their 

 centre. This could not be ; for the focus is at the distance of half the 

 radius. 



Imperfect, however, as the theory appears to have been, there can 

 be no question that the practice of setting fire to substances by placing 

 them in the foci of catoptric and dioptric instruments, was known 

 some centuries before the Christian era. In addition to what is already Socrates, 

 adduced, we may cite a passage from the * Clouds' of Aristophanes, in ? 

 which he introduces Socrates as giving lessons to Strepsiades. The 

 object of the dramatist is to ridicule the philosopher. Strepsiades 

 proposes an expedient by means of which he intends to pay his 

 debts : 



" Strep. You have seen at the druggists that fine transparent stone 

 with which fires are kindled. 



" Soc. You mean glass, do you not ? 

 " Strep. Just so. 



" Soc. Well, what will you do with that ? 



" Strep. When a summons is sent to me I will take this stone, and, 

 placing myself in the sun, I will, though at a distance, melt all the 

 writing of the summons." 



Writing, in those times, was traced on wax spread upon a more 

 solid substance. Hence we see why Strepsiades should propose to 

 melt the writing. 



From this use of burning glasses, the transition to the mirrors, said Archimedes* 

 to have been employed by Archimedes, is not either so extraordinary, JjJJJJjjy 

 or so difficult, as has been usually imagined. It has been repeatedly B.C. 218. 

 affirmed, on the authority of Hero, Diodorus Siculus, Lucian, and 



2 A2 



