Experiments on Artificial Mirages and Tornadoes. 349 



in different rods cannot without further investigation be safely 

 ascribed to differences in the area or shape of their cross- 

 sections. Further, elastic moduli may alter under mechanical 

 treatment, so that it would be unsafe to assume if a hollow 

 bnr were further hollowed or were altered in shape, that its 

 Young's modulus would remain unaffected. 



If it were possible to measure with sufficient accuracy the 

 frequency of the fundamental note and several of its 

 " harmonics " in a single rod, one would have a more certain 

 basis of comparison with the theoretical results. Even in 

 this case, however, there is the consideration that in practice 

 the rod must be supported in some way, and this is likely to 

 introduce some constraint not accurately represented by the 

 theoretical conditions. Again, reaction between the vibrating 

 rod and the surrounding medium may not be absolutely 

 without influence on the pitch *. 



I mention these difficulties because their recognition may 

 prevent a considerable waste of time on the part of anyone 

 engaged in experiments on the subject. 



Though somewhat of a side issue, it may be worth remark- 

 ing that the correction factor l — ^p^ific 2 for the frequency in 

 isotropic material contains no elastic constant except Poisson's 

 ratio. Thus observations made on rods differing only in 

 material might throw some light on the historic question 

 whether rj is or is not the same for all isotropic substances. 



The discussion of equations (6) and of the experimental 

 side of the problem has been largely expanded at the suggestion 

 of the Society's referee. 



XXX. Some Experiments on Artificial Mirages and 

 Tornadoes. By R. W. Wood f. 

 [Plate III.] 



IN an article published in i Nature ' for Nov. 19, 1874, 

 Prof. Everett, in discussing the phenomenon of mirage, 

 showed that the condition necessary for the formation of sharp 

 images in a horizontally stratified atmosphere, is a plane of 

 maximum refractive index, the optical density decreasing as 

 we go above or below this plane in direct proportion to the 

 distance. 



A horizontal or nearly horizontal ray will be bent towards 

 and cross the plane of maximum density, where it changes 

 its curvature and is again bent towards the plane, which it 



* Cf. Lamb, Memoirs and Proceedings Manchester Phil. Society, 

 vol. xlii. part iii. 1898. 



f Communicated by the Author. 



Phil. Mag. S. 5. Vol. 47. No. 287. April 1899. 2 B 



