430 Lord Rayleigh [Jan. 15, 



easily given, and it explains the leading features of the pheno- 

 menon. But, even in the simpler case of sound, an exact calcula- 

 tion which shall take full account of the conditions to be satisfied 

 at the edge, has so far baffled the eiforts of mathematicians. When 

 the obstacle is a sphere, the problem is more tractable, and, in a 

 recent memoir in the ' I^hilosophical Transactions' a solution is given, 

 embracing the cases where the circumference of the sphere is as 

 great as two or even ten wave-lengths. When the sphere is small 

 relatively to the wave-length, the calculation is easy, but the diffi- 

 culty rapidly increases as the diameter rises. The diagram gives 

 the intensity in various positions on the surface of the sphere when 

 plane waves of sound, i.e. waves proceeding from a distant source, 

 impinge upon it. The intensity is a maximum at the point 0° 

 nearest to the source, which may be called the pole. From the pole 

 to the equator, distant 90^ from it, the intensity falls off, and the 

 fall continues as we enter the hinder hemisphere. But at an 

 angular distance from the pole of about 135° in one case and 165° 

 in the other, the intensity reaches a minimum and thence increases 

 towards the antipole at 180°. 



In private experiments the distribution of sound over the surface 

 of the sphere may be explored with the aid of a small Helmholtz re- 

 sonator and a flexible tube, and in this way evidence may be obtained 

 of the rise of sound in the neighbourhood of the antipole. A more 

 satisfactory demonstration is obtained by the method already em- 

 ployed in the case of the disc, the disc being replaced by a globe 

 (about 12 inches in diameter), or by a croquet-ball of about 3J 

 inches diameter. In the former case the burner may be situated 

 behind the sphere at such a distance as 5 inches. In the latter a 

 distance of IJ inches (from the surface) suffices. By a suitable 

 adjustment of the flame, flaring ensues when everything is exactly 

 in line, but the flame recovers when the ball is displaced slightly 

 in a transverse direction. Since the wave-length of the sound is 

 3 cm. and the circumference of the croquet-ball is about 30 cm., this 

 case corresponds to the curve B of our diagram. 



In connection with the mathematical investigation which led to 

 the results represented graphically in Fig. 2, there is a point of in- 

 terest which I should like to mention. The investigation was carried 

 out upon the supposition that the source of sound is at a considerable 

 distance, so that the waves reaching the sphere are plane ; and that 

 the receiver, by which the sound is detected, is situated on the 

 surface of the sphere. At any given position on the surface of the 

 sphere, the receiver will indicate the reception of sound of a certain 

 intensity, which may be read off from Fig. 2. Now the final results 

 assume a form which shows that, if the positions of the source and 

 the receiver are interchanged, the latter will indicate the reception 

 of sound of the same intensity as in the original arrangement. Thus 

 each of the curves in Fig. 2 represents the solution of two distinct 

 2)roblems : the intensity of the sound derived from a distant source 



