188 BELL SYSTEM TECHNICAL JOURNAL 



moments about the mean of binomial and Poisson distributions are 

 expressed in terms of auxiliary moment coefficients with recurrence 

 relations which also appear to be new. 



Extending the Frequency Range of the Negative Grid Tuhe}^ A. L. 

 Samuel. The conventional vacuum tube when adapted for use at 

 ultra-high frequencies carries with it many of the desirable attributes 

 which it possesses at lower frequencies, such for example as its ability 

 to amplify and the ease with which satisfactory frequency stability 

 can be obtained. However, difficulties are encountered because of the 

 effects of the finite electron transit time and because of certain circuit 

 limitations. Methods of circumventing these restrictions are discussed 

 and illustrated by reference to specific tubes. The paper closes with a 

 brief review of recent work directed toward extending the frequency 

 range of the negative grid tube both as an oscillator and as an amplifier. 



Transmission Theory of Plane Electromagnetic Waves}^ S. A. 

 SCHELKUNOFF. This paper deals with transmission theory of plane 

 electromagnetic waves in free space and in cylindrical regions of 

 arbitrary cross section. Transmission properties of such waves can 

 be expressed very simply in the same terms as the properties of electric 

 waves guided by a pair of parallel wires. The earlier parts of the 

 paper are concerned with general theorems and the latter parts with 

 their application to plane waves in metal tubes of circular and rec- 

 tangular cross sections. 



The Empty Lattice Test of the Cellular Method in Solids. ^^ W. 

 Shockley. The cellular method of constructing wave functions for 

 electrons in crystals developed principally by Wigner and Seitz and 

 Slater is tested by applying it to an artificial crystal in which the 

 potential is constant. Knowledge of the exact solutions for this case, 

 plane waves, shows that the cellular method is quite accurate in the 

 first Brillouin zone but may be in error by a factor of two in the second. 

 Hence calculations of occupied levels in Li and Na are probably quite 

 good; for Cu, Ca, diamond, LiF, and NaCl the errors will be larger. 

 Calculations of excited states are likely to be very much in error. The 

 accuracy of the cellular method is shown to improve very slowly with 

 increasing number of continuity conditions. 



Sound Propagation in Ducts Lined with Absorbing Materials}^ L. J. 

 SiVlAN. In ventilator and exhaust systems it is desirable to provide 



11 Jour, of Applied Physics, October 1937. 

 ^^Proc. L R. E., November 1937. 

 ^^Phys. Rev., October 15, 1937. 

 ^^ Jour. Acous. Sac. Amer., October 1937. 



