34 Dr BREWSTER on the Construction of Polyzonal Lenses, 



to diminish, by two inches, the thickness of a lens of glass 26 

 inches in diameter, 5 feet in focal length, and 3 inches thick 

 at the centre. I divide the arc of this lens into three parts, 

 and I make each of these portions of the arc approach to 

 each other concentrically, so that there remains only an inch 

 of thickness at the centre ; and I form on each side a step of 

 half an inch, to bring together the corresponding parts. By 

 this means, in making a second step, I arrive at the extremity 

 of the diameter, and I have a lens with steps, which is nearly 

 of the same focus, and which has the same diameter, and near- 

 ly two times less thickness than the first, which is a great ad- 

 vantage. 



" If we wish, in short, to cast a piece of glass four feet in dia- 

 meter, by two and a half inches in thickness, and to work it by 

 steps to a focus of eight feet, I have computed, that, by leaving 

 one and a half inch of thickness at the centre of this lens, and 

 at the exterior ring of the steps, the heat of this lens will be 

 to that of the lens of the Palais Royal as 28 to 6, without ta- 

 king into account the difference of thickness, which is very 

 considerable, and which I cannot estimate before hand. 



" This last kind of refracting mirror is the most perfect 

 which can be made of its kind ; and even if we should reduce 

 it to three feet in diameter, by fifteen lines in thickness at the 

 centre, six feet in focal length, which would render the execu- 

 tion of it less difficult, we should always have a degree of heat 

 at least four times greater than that of the most powerful len- 

 ses that we know of. I venture to say that this mirror with 

 steps will be one of the most useful instruments in physics. I 

 have contrived it more than twenty years ago, and all the phi- 

 losophers to whom I have spoken of it, are anxious that it should 

 be executed. It might be made highly useful in the promo- 

 tion of science, and by adapting to it a Heliostate, we might 



