Notes. 565 



TFP is the theoretical focal plane. Only one Fraunhofer ring — the inner- 

 most—is represented, and this one only is of any threat practical importance 

 It will be observed that the Fraunhofer ring forms at the focal plane a 

 cone having its apex in that plane. If we assume that it continues to be 

 propagated inward according to the ordinary law of light propagation aloui; 

 rays normal to the wave-front, it will follow that this conical wave-front will 

 continue to contract upon its own axis, and that at a distance determined by 

 the divergence angle of the normal beam it will reach its point of greatest 

 condensation. Fig. 131 shows diagrammatically the production of this result. 

 Now if such a condensation of the focused light takes place in the plane E 

 of fig. 131, it is clear that the image of a point source of light must be better 

 defined in this plane E than in the theoretical focal plane ; from which again 

 it would follow that the effect of Fraunhofer diffraction is not only to impair 

 definition in the focal plane itself, but also to displace the effective focal 

 plane to a position behind that :of the theoretical focal plane. The author 

 proposes as an approximate expression for the extent of this displacement 



a = .— ^ — j where a = the displacement, u - the divergence angle of the 



focused beam, and X = the wave-length of light. This expression, when 



highly magnified images are formed, becomes a = — where M = the scale 



of magnification. 



The theoretical position having been thus defined, its bearing upon 

 certain obscure problems of practical optics was next discussed. First there' 

 is the fact with which every photographer is familiar, that for really critical 

 focusing it is necessary to focus with the particular stop .with which you 

 intend to operate during exposure. Another fact of the same class is that 

 when a Microscope is adjusted for high power work the focus is immediately 

 disturbed by any change in the adjustment of the substage condenser, and 

 that if in this way the angle of the light is altered even slightly, a corre- 

 sponding readjustment of focus becomes necessary. These are matters quite 

 commonly known. The author added an observation recently made by him- 

 self when working with a Microscope arranged to give extremely highly 

 magnified images and fitted with an oscillating screen for increasing the 

 diameter of the emergent pencil. Then it is found that the image seen upon 

 the oscillating screen shows much greater crispness of detail than when seen 

 as an aerial image. 



Supplementing these general observations, the author showed some photo- 

 graphs in which negatives obtained in the theoretical focal plane were com- 

 pared with negatives of the same object obtained in a focal plane displaced in 

 accordance with the expression obtained above for the displacement of the 

 effective focal plane. The results were striking, but not conclusive, and, 

 indeed, the difficulty of determining with exactitude the wave-length of the 

 light which produces a given photograph makes experiment upon these lines 

 much more difficult than would perhaps be expected. The author submit te, 1 

 his results as tentative and immature in their present form, suggesting that 

 they point to a promising field of further investigation. 



An Interference Apparatus for the Calibration of Extensometers. 

 By J. Morrow, M.Sc, and Professor E. L. Watkin, M.A. 



In research work on the elasticity of metals, in which extensometera of 

 considerable delicacy were employed, some difficulty was experienced in 

 determinim? the constants of the instruments with sufficient accuracy, 

 because the mechanical devices with which they could be com] Kind would 



