proceedings: philosophical society 403 



and this analysis would also be correct in the sense that the portion 

 of the wave analysed could be reproduced by combining the compo- 

 nents found by the analysis. We thus see that a Fourier analysis 

 does not necessarily tell anything in regard to the physical apparatus 

 giving rise to the complex sound wave. If, however, the complex 

 wave be explored by a system of tunable resonators the analysis so 

 found does give information in regard to the source. The apparatus 

 exhibited consisted of such a series of resonators. The detecting de- 

 vice is a Rayleigh disc suspended in the opening of the resonator and 

 deflections are measured by a beam of light reflected from the disc. 



Discussion. Mr. Swann raised questions regarding what was really 

 of importance to the ear and whether a physical analysis can be of the 

 same nature as that of the ear's system. In experimental work the 

 mounting and operation of a musical instrument is entirely mechani- 

 cal and without any of the effects due to a player's skill when using the 

 same instrument. The ear apparently appreciates the energy. Mr. 

 C. A. Briggs said that the mechanical receipt of sound by the ear 

 might be explained by the reed frequency indicator. Mr. Curtis 

 suggested that an improvement might be obtained by using a model 

 of the ear's system for experimental work. Mr. Wead called atten- 

 tion to the fact that a large part of detail of the ear's system as gener- 

 ally described is due to handling in cleaning and cutting, and does not 

 correspond to anything in the living ear. In music fixed pitch is not 

 wanted. Mr. Hewlett stated that he hoped to take up later experi- 

 mental work in connection with mechanical playing. 



By invitation, Mr. J. A. Anderson of Johns Hopkins University 

 then presented a paper on Diffraction gratings; their preparation and 

 use. A reflecting diffraction grating consists of a polished plane or 

 spherical metallic surface on which are ruled a great number of lines 

 or grooves, all of which must be straight, parallel, and equidistant 

 from each other. In practice these conditions are never satisfied ab- 

 solutely, and the question arises as to what deviations from ideal con- 

 ditions may exist without impairing the quality of the grating. A dis- 

 cussion shows that the lines should not have a radius of curvature of 

 less than 3 kilometers, and the distance between them should be so 

 nearly constant that the deviation of the last line from its ideal posi- 

 tion should not exceed one-quarter of a wave-length. The design and 

 construction of a machine for ruling perfect gratings is a very difficult 

 problem, but it was solved so completely by Professor Rowland that by 

 following him intelligently it does not now present any insurmountable 

 difficulties. The parts of the machine must be carefully tested; 

 methods for doing this were explained. The machine is finally tested 

 by the method of "cross rulings," a method devised by Prof essor Row- 

 land, and Which is so sensitive that errors in spacing as small as 



o Qrvr. r>An inch can be detected with ease. 



j| Discussion. Following the exhibit of a number of gratings and 

 cutting tools Mr. Abbot asked regarding the life of a ruling tool and 



