236 FERGUSON'S LECTURES. 



LECT. point or principal focus /, whose distance is equal to 

 ^ij^, the radius or semidiameter of the sphere of the glass's 

 convexity. But if a glass be more convex on one side 

 than on the other, the rule for finding the focal distance 

 is this : as the sum of the semidiameters of both con- 

 vexities is to the semidiameter of either, so is double the 

 semidiameter of the other to the distance of the focus. 

 Or, divide the double product of the radii by their sum, 

 and the quotient will be the distance sought. 



Since all those rays of the sun which pass through a 

 convex glass are collected together in its focus, the force 

 of all their heat is collected into that part ; and is in 

 proportion to the common heat of the sun, as the area 

 of the glass is to the area of the focu-s. Hence we see 

 the reason why a convex glass causes the sun's rays to 

 burn after passing through it. 



All these rays cross the middle ray in the focus f y 

 and then diverge from it, to the contrary sides, in the 

 same manner FfG, as they converged in the space 

 DfE in coming to it. 



If another glass F G, of the same convexity as D E, 

 be placed in the rays at the same distance from the 

 focus, it will retract them so, as that after going out of 

 it, they will be all parallel, as a b c, and go on in the 

 same manner as they came to the first glass DE, through 

 the spate ABC; but on the contrary sides of the mid- 

 dle ray Bfb: for the ray A Df will go on from / in 

 the direction fG a, and the ray C Ef in the direction 

 f Fc ; and so of the rest. 



The rays diverge from any radiant point, as from a 

 principal focus : therefore, if a candle be placed at /', 

 in the focus of the convex glass F G, the diverging rays 

 in the space FfG will be so refracted by the glass, as, 

 that after going out of it, they will become parallel, as 

 shewn in the space c b a. 



If the candle be placed nearer the glass than its 

 focal distance, the rays will diverge after passing 



