4 Professor Airy on the Spherical Aberration 



insensible. In this instance, then, it would be proper to attend 

 to the first condition. But in all cases of micrometer measurement, 

 in which the power is not very great, distortion is of little con- 

 sequence, the object and the wires being equally distorted; but 

 it is important that the object and the wires should be seen dis- 

 tinctly in all parts, without pushing or pulling the eye-piece. Here 

 then the second condition should be insisted on, and the third, 

 if possible, combined with it. For a telescope, which is used for 

 examining the disc of a planet, or any similar observation without 

 instrumental measurement, the third condition is quite as important 

 as the second : the first less so. For common perspective glasses, 

 opera glasses, &c. regard ought to be paid to all three, but especially 

 to the first. I shall take occasion to apply the formulte to the con- 

 struction of the camera obscura: the second and third conditions 

 ought there to be enforced, except the sacrifice of the first is very 

 great. 



The same causes which divide the effects of spherical aberration 

 into three distinct parts, oblige us to use, for 'the investigation of 

 these parts, three distinct operations. I shall, therefore, inves- 

 tigate, 1st, the course of the axis of a pencil; 2d, the point of 

 convergence of rays in the plane passing through the axis of the 

 jiencil and the axis of the lens; 3d, the point of convergence of rays 

 in the plane perpendicular to the former, and passing through the 

 axis of the pencil. 



It is evident that an object will be seen without distortion if 

 its image, exactly similar to the object, be formed on a plane ; and 

 then the trigonometrical tangent of the angle, made with the axis 

 of the lens by the axis of the pencil after refraction, will bear to 

 the tangent of the angle before refraction a constant ratio : if the 

 ratio be not constant, its difference from a constant ratio will 

 indicate the degree of distortion. This suggests the following 

 Propositions. 



