aiul Distrihition of Sound, 291 



of the speaking-trumpet, or (by the hiw of reciprocity, 

 §§ 101>, 294:) hearino-trumpet. It' the diameter of the large 

 open end be small in comparison with the wave-length {^Tr/k), 

 the waves on arrival suffer copious reflexion, and the ultimate 

 result, which must depend largely on the precise relative 

 lengths of the tube and of the wave, requires to be determined 

 by a different process. But by sufficiently prolonging the 

 cone, this reflexion may be diminished, and it will tend to 

 cease when the diameter of the open end includes a large 

 number of wave-lengths. Apart from friction it would 

 therefore be possible by diminishing w to obtain from a given 

 source any desired amount of energy, and at the same time 

 by lengthening the cone to secure the unimpeded trans- 

 ference of this energy from the tube to the surrounding air. 



'•From the theory of diffraction it appears that the sound will 

 not fall off to any great extent in a lateral direction, unless 

 the diameter at the large end exceed half a w^ave-length. 

 The ordinary explanation of the efi^ect of a common trumpet, 

 depending upon a supposed concentration of rays in the axial 

 direction, is thus untenable.'^ 



Data respecting Foe/Signals, 



The above theory should throw light upon the jDroduction 

 of sound in " fog-signals/' wdiere sirens, or vibrating reeds, 

 are associated with long conical trumpets. In the practice 

 of the Trinity House these are actuated by air compressed to 

 a pressure (above atmosphere) of 25 lbs. per square inch, or 

 1760 gms. per sq. cm., a pressure which appears rather high. 

 According to Stone the highest pressure used in orchestral 

 wind-instruments is 40 inches (102 cm.) of w^ater. 



As might be expected from the high pressure, the energy- 

 consumed during the sounding of the signal is very con- 

 siderable. The high note of the St. Catherine's Service signal 

 takes 130 horse-powder, and the corresponding note of a 

 Scottish signal (tested at St. Catherine's in 1901) requires 

 as much as 600 horse-power. The question obtrudes itself 

 whether these enormous powers are really utilized for th.'^ 

 production of sound, or whether from some cause, possibly 

 unavoidable, a large proportion may not be wasted. 



Comparison with Musical Instruments ^'C, 



These statements as to horse-power may be better appre- 

 ciated if I record for comparison the results of some rough 

 measurements, made in 1901, upon the power absorbed by 

 smaller instruments. In the calculation it will suffice to 

 regard the compressions and rarefactions as isothermal. 



U2 



