a6a Aberration. [Book III. 



nal aberration N F in the firft cafe will be to that of 

 w F in the fecond as the cube of P H to the cube 

 of p E. 



Philofo>hers, confidering the errors to which they 

 were thus expofed by the fpherical form of their 



For mgs=D G EG X Sin. GED:=E GxS. 

 EG HExCos. HEG HExS. H4E. 

 3. li I, E. 



. EH. 



but S. H b E varies, as S. E b I and E b is a ccnftant quantity. 



.-. mg varies as sTLT^Tj 3 , that is as JIT, 3 , that is as 

 Semi- aperture] 3 . 



If the line mg be now fuppofed to move parallel to itfelf on the 

 axis C F, and to be made proportional in every place to the cub 

 of the femi- aperture, a curve will be formed to which the refracted 

 rays will be tangents, and as the adjacent rays crofs each other in 

 the points m, or the extremities of the ordinate ; the light in thefe 

 points will be ilronger than within its area ; and the curve thus 

 formed, which experiment mews to us in various inftanccs, i 

 called a cauftick. 



All the rays incident on the furface b C will pafs within the 

 fpace mg, and consequently if the rays of the fun are refraded by 

 a concave furface, and received by an opake body perpendicular to 

 the axis at the diftance C^, a circle of light will be formed, whofe 

 denfity is greater at the circumference and lead at its center. But 

 thcugh all the refrafted rays will pafs through the area of a circle 

 at the d'ilance C^, whofe diameter is m /, they will, at a greater 

 diftance from the furface, pafs through a much fmaller circle /, 

 which, when it is the leaft, is called the circle of lead diffufion, 

 and in this circle the denfity of rays, and ccnfequently the heat, 

 is the greateft. In this circle the denfity of the rays will be the 

 greatelt in the center, and it decreafes between the center and the 

 circumference to<a place where it is a minima n, and confequently 

 increafes again to the circumference. The inveftigation of this 

 property would carry us too far into the abiUufe mathematics ; but 

 what hm.-'bpen faid fufficiemly fliews the nature of the diftufion of 

 the rays u ' ht from the figure of the furface, which is now 

 Known to occaiion a much greater error, in proportion to that 

 arifing fiom refrangibility, than was flippofed by cur nift phi- 

 Ipfojpher. 



glafles, 



