756 



SILVANUS P. THOMPSON. 



of the horizontal rod this ring contracts, becomes a mere spot in the 

 middle of the coma ; and then disappears. À coarse grating made of a 

 number of parallel horizontal wires held across the beam casts as its 

 shadow a séries of approximately concentric rings, as shown at E in 

 Fig. 6. 



Paradox B. 



The shadow of a vertical line is a cross. The disposition of the lens 

 remaining unaltered, let the rod or wire be set upright, and let it be 

 removed fnrther from the lens ; in fact a little beyond the place where 

 the conjugate focus of the lamp would be if the lens were not tilted. 

 If the rod stands npright, intersecting the axis of the beam, its shadow 

 will be a cross, of which the two latéral arms bend downwards as in 

 Fig. 6_, B. This elfect is rnainly due to the présence of ordinary sphe- 

 rical aberration. 



Experwierd 6. Instead of using as in thèse two paradoxical disposi- 

 tions an opaque wire or rod, thèse may be nsed a narrow slit formed by 

 pasting upon a sheet of glass two pièces of paper with their adjacent 

 edges 2 or 3 millimètres apart. The effect npon the screen, giving the 

 ring of Paradox A, or the cross of Paradox B as a luminous image on 

 a dark background is more striking. 



With this de vice the two following Paradoxa are better shown than 

 by the use of an opaque rod or wire. 



Paradox C. 



The shadow of a horizontal line is a figure of eight. To procure this 

 resuit the following disposition was made. The plano-convex lens was 

 placed at about -15 centimètres from the source of light, with its convex 

 face toward the light. It was then tilted about 30° out of the vertical 

 position its upper eclge being shifted toward the light. The white 

 screen to receive the images was placed about 250 centimètres from the 

 lens. The narrow slit above-mentioned (or, less favourably, a straight 

 rod or wire) was then held horizontally across the path of the light at 

 about 53 centimètres beyond the lens. The shadow cast on the screen 

 is an 8. If the horizontal object is held nearer to the lens or further 

 away the from of the shadow undergoes modification. If held nearer 



