ii8 



NATURE 



{Dec. 12, 1878 



a source near the ground is, therefore, not heard far off 

 by an observer standing on the ground. It is heard at a 

 much greater distance if the observer or the source of 

 sound be in an elevated position. The state of the atmo- 

 sphere will have great influence upon these conditions. 

 In dry air and sunshine the deflection of sound upwards 

 will be greater than in moist air which forms clouds above, 

 or during rain. 



The decrease of temperature in the upper strata of 

 the atmosphere causes sound to travel at a lesser speed 

 than in the lower ones. Now if a wind is blowing, the 

 velocity of which increases with the height, then, as 

 Prof. Stokes remarks, this causes an increase in the 

 velocity of the sound-waves in the direction of the wind, 

 and a decrease in velocity in the opposite direction ; thus, 

 for sound which travels in the former direction, the re- 

 tarding effect of decrease of temperature is neutralised, 

 and for that travelling in the latter it is augmented. We 

 therefore hear better if the wind blows towards us from 

 the source of sound than if the contrary takes place. 

 Indeed, by an upper windy layer, sound produced in the 

 lower tranquil air may be totally reflected. This influence 

 of wind is remarkable also because it forms an exception 

 to the law demonstrated by myself, viz., the law of reci- 

 procity in the propagation of sound, if the sound-source 

 and the observer change places. 



The problems of the reflection of sound by fixed walls, 

 for instance, the pheHomena of whispering-galleries, 

 speaking-trumpets, and the echo, are treated in the same 

 manner. Although here the admissibility of the decom- 

 position of sound into sound-rays does not, as a rule, 

 appear quite so unquestionably justified, yet the pheno- 

 mena observed agree with this hypothesis on the whole. 



An essential progress in the application of the theory 

 upon experiments has been made by the author in the 

 calculation of the influence of the open apertures of organ 

 pipes and resonators upon their pitch. In my own demon- 

 stration of this part of the theory I had started from those 

 forms of motion which did not render the calculation too 

 difficult, and had then derived the corresponding forms of 

 pipes ; finally, I had so determined the optional constants 

 of my hypotheses, that the form of pipe approached the 

 form wished for, the cylindrical one, for instance ; yet I 

 remained confined to a few forms if I did not wish to 

 complicate the calculation too much. Lord Rayleigh, on 

 the contrary, supposes a given form of pipe, and has 

 employed the maxims, developed in the first volume of 

 his work, regarding the variation of conditions under which 

 sound-motion takes place, to determine the limits within 

 which the true value of the desired magnitude must lie, 

 and has indeed been able to draw these limits so narrowly 

 for the most important problems, like that of the cylin- 

 drical open pipes, that practically the solution is perfectly 

 sufficient. In this way he has been able to treat simul- 

 taneously a number of problems, which hitherto had not 

 even received an approximate solution, for instance, the 

 determination of the proper tones of resonators of the 

 shape of bottles with wide body and narrow neck. 



Besides the problems mentioned, which are of direct 

 importance to experimental physics, a series of others 

 are worked out, where the mathematical solution can be 

 completely given, such as the propagation of sound in 

 balls, spherical layers and rectangular boxes filled with 



gas, the reflection of sound from the outer surface of a 

 ball, and the communication of sound to air by oscillating 

 balls and strings. These problems are valuable not only 

 as theoretical exercises, but also with regard to our under- 

 standing of physical phenomena. They are examples 

 affording to the mental eye of the physicist a particularly 

 perfect insight into the essence of sound-motion and the 

 changes it undergoes, when the conditions under which 

 it occurs are changed. Thus he obtains quite as good a 

 conception of the typical behaviour of sound as if he had 

 actually seen the phenomena, and this conception will 

 also guide him safely in cases of observation, where the 

 exterior conditions are not as simple as they are in the 

 theoretical example. 



At the end of the volume Lord Rayleigh has placed the 

 words : "The End." We hope that this maybe only the 

 provisional, not the definite end. There is still an im- 

 portant chapter wanting, viz., that on the theory of reed- 

 pipes, including the human voice. For the former, at 

 least, the principles of their mechanics can already be 

 given, and the methods the author employs seem to me 

 to be particularly well adapted for further progress in 

 these domains. 



After reed-pipes we would mention the theory of singing 

 flames, and the blowing of organ-pipes. In the latter 

 case the leaf-shaped current of air, which comes from the 

 wind-case, forms a sort of reed, which oscillates under 

 the influence of the oscillating column of air in the interior 

 of the pipe, and which throws its air now into the interior 

 of the pipe, and now outside. 



'j' Altogether, the whole of this important class of motions, 

 where oscillatory movements are kept up through a cause 

 which acts constantly, deserves detailed theoretical con- 

 sideration. The action of the violin bow, and the 

 sounding of the ^olian harp, also belong to this class. 



Lord Rayleigh certainly deserves the thanks of all 

 physicists and students of physics ; he has rendered them 

 a great service by what he has done hitherto. But I 

 believe I am speaking in the name of all of them, if I 

 express the hope, that the difficulties of that which yet 

 remains will incite him to crown his work by completing it. 



H. Helmholtz 



OUR BOOK SHELF 



Zoologischei- Anzeiger. Herausgegeben von Prof. J.Victor 

 Carus. (Leipzig : Wllh. Engelmann.) 



The idea of a zoological "advertiser" seems to us a most 

 excellent one, and we both welcome and heartily recom- 

 mend to our readers who are interested in the animal 

 kingdom this little fortnightly journal of Prof. Carus. 

 The editor purposes to publish a number every two 

 weeks, each number to contain from sixteen to eighteen 

 pages, and the yearly subscription to be six shillings. 

 The first number bears the date of July i, 1878, and 

 already a dozen numbers have appeared. The plan of 

 each number is to commence with a retrospect of the 

 current literature of zoology, a retrospect that we need 

 hardly say will be well done by one so learned and able 

 in the matter of bibliography as the editor of that most 

 necessary work, the " Bibliotheca Zoologica." Then 

 each number contains some short notices on zoological 

 subjects in connection with museums, chiefly such as 

 have a practical bearmg. Thus in No. 2 we find an 

 article by G. von Koch, of Darmstadt, on a method by 

 which sections can be made of substances of different 



