432 Lord Bayleigh [Jan. 15, 



and detected at any point on the surface of the sphere ; and 

 the intensity of the sound derived from a source on the surface of 

 the sphere, and observed at a distant point. This result forms an 

 interesting example of a principle of very wide application, which I 

 have termed the Principle of Reciprocity. Some special cases were 

 given many years ago by Helmholtz. 



It is a matter of common observation that if one person can see 

 another, either directly or by means of any number of reflections 

 in mirrors, then the second person can equally well see the first. 

 The same law applies to hearing, apparent exceptions being easily 

 explained. For instance, such is the case of a lady sitting in a 

 closed carriage, listening to a gentleman talking to her through the 

 open window. If the street is noisy, the lady can hear what the 

 gentleman says very much more distinctly than he can hear what 

 she replies. This is due to the fact that the gentleman's ears are 

 assailed by noises of the street from which the lady's ears are 

 shielded by the walls of the carriage. 



Another instance may be mentioned, which will appeal to elec- 

 tricians. In the arrangement known as Wheatstone's bridge, re- 

 sistances are joined in the form of a lozenge, a galvanometer being 

 connected between two opposite angles of the lozenge, w^liile a bat- 

 tery is connected between the other two angles. When the resist- 

 ances are suitably adjusted, no current flows through the galvanometer; 

 but a slight want of adjustment produces a deflection of the gal- 

 vanometer, thus indicating the passage of a small current, ^ow, 

 if the positions of the battery and the galvanometer are interchanged, 

 without alteration of resistance, the same current as before will flow 

 through the galvanometer, and therefore the deflection will be the 

 same as before. Thus with a given cell, galvanometer and set of 

 resistances, the sensitiveness of the Wheatstone's bridge arrangement 

 is the same whichever pair of opposite angles of the lozenge are 

 joined by the galvanometer. If a source of alternating E.M.F. is 

 used instead of the battery, and a telephone is substituted for the 

 galvanometer, then the j^rinciple of reciprocity still applies, whether 

 the resistances are inductive or non-inductive. 



A simple illustration, of a mechanical nature, is now shown. 

 Fig. 3 represents a straightened piece of watch-spring clamped at 

 one end to a firm support. A weight can be hung at either of the 

 points A or B of the spring, vsrhen it may be observed that the de- 

 flection at B due to the suspension of the weight at A, is exactly 

 equal to the deflection at A due to the suspension of the weight at B. 

 This result is equally true wherever the points A and B may be 

 situated ; it applies not only to a loaded spring, which has been 

 chosen as suitable for a simple lantern demonstration, but also to any 

 sort of beam or girder. 



It will have become clear, from what has been said, that waves 

 encounter considerable difficulty in passing round the outside of a 

 curved surface. I wish now to refer to a complementary pheno- 



