472 Dr. 0. V. Drysdale on the 



Finally it is shown by analogy with the ripples that the 

 wave-fronts diverge in expanding spheres, becoming less 

 curved as they recede from the source, and ultimately plane, 

 and that the direction of propagation is perpendicular to the 

 wave-front ; and the difference between plane, divergent, 

 and convergent waves is illustrated. At the same time, it 

 may be pointed out with advantage that i£ the medium were 

 'not isotropic, the speed of propagation would be different in 

 different directions, the wave-front being ellipsoidal and not 

 perpendicular to the lines of propagation. The writer has 

 never found that elementary students have any difficulty 

 over this, and it prepares the way for subsequent work in 

 polarization, &c. 



The next stage is to explain the formation of shadows and 

 of an image by a pinhole, referring at the same time to 

 diffraction. The formation of the penumbra may also be 

 well illustrated by waves, and photometry explained by 

 showing that any portion of the wave-front carrying a 

 certain amount of light-energy expands proportionally to the 

 square of the distance from the source. 



The study of reflexion at plane surfaces comes next, first 

 with plane and then w T ith spherical waves, proving the laws 

 of reflexion, application to various instruments, measurement 

 of angles of a prism, &c, and formation of images by one or 

 more plane mirrors. 



Curvature and its Measurement.- -At this stage the ideas 

 and units of curvature are introduced, explaining the necessity 

 for the measurement of the curvatures both of waves and of 

 reflecting surfaces. Students will easily realize that a 

 satisfactory definition of curvature is the reciprocal of the 

 radius, but it may be proved from the ordinary definition of 

 curvature if preferred. The dioptre with its multiples and 

 submultiples may then be introduced and the relations : 



. ,. ' 1 100 39-37 



curvature in dioptres = —7 — t r = —, r = — 77—, 



v r (metres) r (cm.) r" 



and the corresponding conversions from curvatures to radii. 



Practical curvature measurement may then be taken up, 

 the equality of the products of the segments of any two 

 chords of a circle being demonstrated either by geometry or 

 by simple measurement, and from this the ordinary sphero- 

 meter formula 



<? + ¥ -r 27, 2 



when the curvature is small. When c and h are in millimetres 



