$40 On the Catoptricdl and Dioptrical 



uncertain, and might, change every minute. In order then, 

 that Archimedes might succeed, it was absolutely necessary, 

 cither that he should be provided with a great number of 

 burning minors of different local distances, or with one 

 onlv, the focal distance of wheh he could augment or di- 

 minish at pleasure. Other vvise his success would have been 

 left to accident; for, if the distance of the ships changed 

 while he was directing his mirror towards them, he ran the 

 risk of embarrassment, if he could not have altered its fo- 

 cal distance. Now the focal distance of concave mirrors 

 being invariable, it is plain that if Archimedes had wished to 

 use such, and had not made the distance of the focus ex- 

 actly equal to that of the ships from the mirror, he would 

 have lost all his time, trouble, and expense. 



76. " But by using plane mirrors, his machine would have 

 always answered equally well. If he had mistaken the di- 

 stance of his object, he could have easily remedied the 

 error, by only changing the position of his component 

 plane mirrors. , 



77- (i From what has now been said, it follows, that if it 

 be true, as Tzetzes assures us it is, that the component mir- 

 rors of Archimedes were moveable, it is also proved that 

 they vvere plane; and consequently the invention of raising 

 flame by plane mirrors is as antient as the days of that 

 philosopher*. 



- 78. " In the second place, it is not certain, that the 

 burning mirrors of the antients were necessarily metallic; 

 for T shall presently prove, that they might have been of 

 glass. 



70 ff Thirdly, M. de Fontenelle positively affirms that the 

 antients were ignorant of the power of glass globes to mag- 

 nify objects. So much indeed was he persuaded of this, 

 that he labours to prove why they were unacquainted with 

 this property of glass globes, while they knew their power 

 of burning. The truth is, that they were equally well ac- 

 quainted witb both these properties; as is proved by this 

 passage from Seneca {Natural Quest, lib. i. cap. 6.) Lit era 9 

 qitamvis minutes at obscures, per vitream pilam, agues pU* 



f This arrurr.cnr, which I could not put into fewer words, without 

 entirely departing frpm rhc original, is. as J t-ke it. perfectly conclusive. 

 It is, however, ijarural for me to think so; foi as far aa motion is co0- 

 cerned,thervasaning is the tattle, mutatis mw n!'s, with that by wh'ch I 

 endeavoured ro prove {§ 24 of my 2d iett ) that vvhipn R Bacon talks of* 

 making '.he sun, &c. appear to us to be over the heads of our enemies, 

 anyopr.cal instrument contrived r o produce this effect on aft enemy always 

 in movicn, must itself be moveable. — Translator. 



5 nam, 



