750 



SILVANUS P. THOMPSON. 



posterior surface being concave. Thèse conditions are clearly incom- 

 patible with one another. In fact a system of centred lenses having at 

 least four radii of curvature must be resorted to if botli conditions are 

 to be even approximately fulfilled. No single lens then, of whatever 

 shape can be free from both central and zonal aberration, even for 

 parallel beams of liglit. Even if it is corrected for central aberration its 

 différent zones would produce at the centre of the field images, say of 

 the sun or other distant object of apparent magnitude, vvliich are of 

 différent sizes, and which by their overlapping produce a bad définition. 

 Still worse is tlie image produced by an oblique pencil, because the 

 émergent pencil is no longer homocentric. Its rays still surround its cen- 

 tral oblique axis; but the rays from above and below that axis meet one 

 another at a différent distance (from the lens) from that at which the 

 rays from right and left meet one another. The méridional and sagittal 

 sections of the pencil possess, in fact, différent angles of convergence. 

 The resuit is the distorted coma which takes the place of the stigmatic 

 point-image. 



In the experiments now to be described the phenomenon of the coma 

 itself were examined without regard primarily to the question how far 

 it was due to purely zonal or how far to uncorrected central aberration. 



The lens first used was a plano-convex having an aperture 19 centi- 

 mètres in diameter, and a focal length of about 50 centimètres. As 

 source of light an arc lamp was used, projecting a horizontal beam, in 

 some cases with condenser lenses in front to render the beam more or 

 less parallel as desired. The plano-convex lens was placed in front of 

 the lantern. It was so mounted that it could be tilted about its horizon- 

 tal diameter to any desired angle, so that the axis of the incident beam 

 might meet it at any desired degree of obliquity. The space beyond the 

 tilted lens was then explored by means of a white semi-transparent screen 

 set vertically so that the axis of the beam met it normally. 



Experiment 1. The incident beam having beenrendered nearly parallel, 

 and the lens being adjusted to centre with its flat face toward the light, 

 the transparent screen was set at the principal focus of the lens. The 

 lens was then tilted around its horizonal diameter to about 25°, the upper 

 edge of it being farthest from the lantern. The luminous image spread 



