138 BELL SYSTEM TECHNICAL JOURNAL 



visualize in its entirety. In war, when practically every phase of the na- 

 tional effort to overthrow the Axis aggressors depends in some part on swift 

 communication, both the extent and the importance of the System's con- 

 tributions to the winning of the conflict are beyond summarizing. In the 

 past two years, numerous articles in the Bell Telephone Magazine (listed at 

 the end of this article), and in the employee publications of the Associated 

 Companies, have described many aspects of the System's cooperation with 

 the armed forces, with industry, and with the civilian population. Now, 

 nearly a year after Pearl Harbor, it seems appropriate to review both the 

 System's preparations for the national emergency and the steps which it has 

 taken since war became no longer a threat but a fact. To the extent that 

 it is possible in limited space, this article rounds out the previous frag- 

 mentary parts of the whole picture. 



The Number of Two-Terminal Series-Parallel Networks} John Riordan 

 and C. E. Shannon. This paper is concerned with the number of ways 

 n abstract (electrical) elements may be connected in series-parallel arrange- 

 ments and in particular with the way the number behaves for n large. After 

 a proof of a generating identity for the numbers given without proof by P. 

 A. MacMahon in 1892, the paper gives recurrences and schemes of computa- 

 tion by means of which MacMahon's table for the numbers is extended from 

 w = 10 to w = 30. The behaviour for n large is shown to be of the form 



with A a fixed constant and X a real number between 2 -f- \/2 = 3.414 

 and 4 and closer to the former than the latter; indeed an approximating 

 function for which X is about 3.56 agrees with the numbers within 3% over 

 the range 7 to 20. These results are used to show that almost all switching 

 functions of n variables require at least 



(1 - e) — 6 > 



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switching elements (make or break contacts) in series-parallel realization. 



The Electrical Oscillations of a Perfectly Conducting Prolate Spheroid.^ 

 Robert M. Ryder. The forced oscillations of a perfectly-conducting pro- 

 late spheroid of eccentricity nearly unity are shown to be decomposable into 

 "harmonics" corresponding to different modes of vibration, each harmonic 

 being quantitatively connected with a certain portion of the impressed elec- 

 tric field which drives the antenna. The harmonics contribute additively 

 to the current and field of the spheroid; each offers a characteristic imped- 



^ Jour. Mathematics and Physics, August 1942. 

 ^Jotir. Applied Physics, May 1942. 



