VOL. LII.] PHILOSOPHICAL TKANSACTIONS. ^ 5] 7 



where, by the violent circular motion of the air, it was immediately hurled into 

 ten thousand pieces, and scattered to great distances on all quarters, except that 

 from which the wind proceeded. And it further appears, that the violence of 

 the wind in that place was over as soon as the house was taken up; otherwise no 

 person could have been left on the floor. 



IV. A Theorem on the Aberration of the Rays of Light Refracted through a 

 Lens, on Account of the Imperfection of the Spherical Figure. By the Rev. 

 Nevil Maskelyne, F. R. S. Dated from Prince Henry , St. Helens Road, 

 Jan. 16, 1761. p. 17. 



About 2 years since, becoming acquainted with Mr. Dollond's curious disco- 

 very in optics, of correcting the aberration of the rays of light arising from the 

 different refrangibility of the different sorts of rays, by a combination of 2 dif- 

 ferent kinds of glass; and learning from him in conversation that he had invented 

 a theorem, showing the quantity of the aberration of the rays refracted through 

 a lens, on account of the imperfection of the spherical figure; by the applica- 

 tion of which, he was able to make the aberrations of the combined concave and 

 convex object lenses perfectly equal to, and consequently to correct each other; 

 Mr. M. was desirous of being more minutely acquainted with this further great 

 improvement in optics; and Mr. Dollond accordingly readily offered to gratify 

 his curiosity. But in the mean while that Mr. D. was looking over his papers, 

 in order to lay them before Mr. M., Mr. M. having leisure, set about the investi- 

 gation of a similar theorem himself; which having completed, he interchanged 

 with Mr. Dollond for his theorem. The theorems, though similar, were not 

 exactly the same; but by reduction to the same form Mr. M. inferred Mr. D.'s 

 theorem from his, which gave hiifi a further confidence of the exactness of both. 



Let the form of the lens assumed, in the investigation of the theorem, be a 

 meniscus, the radius of whose convex surface is greater than that of its concave 

 surface; and the centre of the two surfaces lie on the same side of the lens as 

 the radiant point, from which the rays diverge that fall on it. The ray falling 

 on the extreme part of the lens v^^ill, after refraction, diverge from a point before 

 the lens, nearer to it than the geometrical focus of rays diverging from the same 

 radiant point, and passing indefinitely near the vertex. 



Let Q express the distance of the radiant point, before the lens, from its vertex j 

 B, the radius of concavity of the surface on which the rays first fall ; and r, the 

 radius of convexity of the second surface; f, the principal focus, or the focus of 

 parallel rays, which will be on the same side of the lens as the incident rays; 

 because r, the radius of the concave surface, is supposed less than r, the radius 

 of the convex surface. Let the ratio of m to n be the same with that of the sine 

 of incidence to the sine of refraction of rays passing out of air into glass, and 



