178 BELL SYSTEM TECHNICAL JOURNAL 



signal-to-noise ratio is improved, greater economy of spectrum space is 

 obtained, the number of tubes required is materially reduced through the 

 use of a common intermediate-frequency amplifier for a number of channels, 

 and any impairment due to the instability of the carrier or oscillator fre- 

 quency is reduced. 



As an example of the possible application of the principles outlined, a 

 hypothetical eight-channel transmission system is described. 



The Physical Significance of Birkhoffs Gravitational Equations}^ Her- 

 bert E. Ives. Birkhoff's gravitational equations are put in terms of dt in 

 place of the local time ds used by him. The transformed equations show that 

 Lorentzian mass has been used, and to the Newtonian attractive force is 

 added a force normal to the direction of motion, vVc^ times the component 

 of the gravitational force normal to the motion. 



Attenuation and Scattering of High-Frequency Sound Waves in Metals and 

 Glasses}^ W. P. Mason and H. J. McSkimin. By using a pulse method, 

 attenuation and velocity measurements have been made for aluminum and 

 glass rods in the frequency range from 2 to 15 megacycles. The sound 

 pulses are generated by crystals waxed to the surface of the rod. This wax 

 joint limits the band width of the transmitted pulse and measurements are 

 made using long pulses which approach steady state conditions. The re- 

 flected pulses show evidence of several normal modes which can be minimized 

 by using specially shaped electrodes. Longitudinal waves show delayed 

 pulses of smaller magnitude that are caused by the longitudinal wave break- 

 ing up into reflected longitudinal and shear waves at the boundary. This 

 effect is small if the diameter of the rod is 20 wave-lengths or more. 



The measured losses for aluminum rods show a component proportional 

 to the frequency and another component proportional to the fourth power 

 of the frequency. The first component is the hysteresis loss found for most 

 solid materials. The component proportional to the fourth power of the 

 frequency is caused by Rayleigh scattering losses which are the result of 

 differences in the elastic constants between adjacent grains caused by 

 changes in orientation. Calculated scattering losses agree quite well with 

 the measured values. The fourth-power scattering law holds quite well 

 until the grain size is equal to one-third of a wave-length. For higher fre- 

 quencies the scattering loss increases more nearly with the square of the 

 frequency. Glasses and fused quartz have a loss directly proportional to 

 the frequency, showing that any irregularities must be of very small size. 



The Growth of Auditory Sensation}"^ W. A. Munson. The integration of 

 sensation with respect to time was studied experimentally by means of tones 



'"PAyj. /?«;., :\ugU8t 1,1947. 



^^ Jour. Acous. Soc. Amer., May 1947. 



^^ Jour. Acous. .Soc. Amer., July 1947. 



