Instruments of the Antients. 245 



must of necessity degenerate into concavity or convexity. 

 Yet when the diameter of their curvature is very great, and 

 their spherical figure perfect, they ought to be considered as 

 perfectly plane. An easy and sensible proof of this is, that 

 none of our mirrors can be considered as more plane, even, 

 and regular, than the surface of perfectly tranquil water. 

 Yet this surface is really convex, the diameter of its con- 

 vexity being the same with that of the globe. But a dia- 

 meter of convexity of some hundred fathoms, is sufficient to 

 denominate our spherical mirrors, plane ones. 



90. " Let us now endeavour to make it appear, from what 

 has been said in this memoir, that the existence of the mir- 

 ror of Ptolemy is very probable ; and for this purpose, each 

 of the two following considerations is more than sufficient. 



91. " First, It cannot be doubted, that in a city so power- 

 ful, opulent, and flourishing as Alexandria was in the days 

 of the Ptolemy s 9 mirrors were very numerous, and even 

 very large*. It appears from history that Alexandria was 

 then the centre of the arts and sciences; the liberality of the 

 Ptolemy s having attracted to it the most learned men and 

 the most skilful artists. 



92. " Without either granting or refusing to the Alexan- 

 drian arts and sciences, such perfection as the intentional fa- 

 brication of such a mirror would require, I say that it is 

 no way contrary to probability, that in the great number of 

 mirrors in that city, some one should be found of a conca- 

 vity sufficiently regular, and whose focus, in some circum- 

 stances, might become sensible by its effects. 



93. " This being so, there is nothing extraordinary in con- 

 ceiving, that some philosopher or artist, happening to stand 

 favourably with regard to the mirror and distant objects, 

 should see those objects larger, and more clearly and di- 

 stinctly, than with his naked eye ; and that, after several 

 trials, he should find the spot from which the effect was the 

 greatest. 



94. " Whether the cause of this phaenomenon was known 

 or not, is a matter of indifference, and could not hinder the 

 knowledge of the effect, which must have been regarded as 

 wonderful; especially if the cause was unknown. Such a 

 mirror must have been looked upon as a present worthy of 

 Ptolemy Euergetes, who having been so great a protector of 

 the sciences, and a lover of curiosities, would recompense 

 the donor magnificently. And it is extremely natural to sup- 

 pose, that he would place it in that superb edifice, the Pha- 



* See § 83, above. 



Vol. 19. No. 75. August 1804. S ros, 



