TABLES OF PHASE 749 



monograph both in degrees and radians for values of/ greater than /o 

 as well as for/ less than/o . The tabular intervals are 0(0.001) 0.600 

 (0.0005) 0.9000 (0.0001) 0.9940 (0.00005) 0.99800 (0.00001) 1.00000. 

 These intcr\'als were selected to permit linear interpolation for intermedi- 

 ate values of the phase to an accuracy of the same order as the accuracy 

 of the tabulated values, i.e., ±1 in the last place. The original Journal 

 article discussed the construction of the tables and the errors involved 

 in the numerical evaluation of Integral (1), described and illustrated 

 the use of the tables, and gave five-place tabulations of the integral. 

 I'his entire article is therefore included in Monograph 2550 for complete- 

 ness along with the newer seven-place tables. 



B. A. Kingsbury^ has pointed out that the Integral (1) which is tabu- 

 lated in the phase tables in question is useful in other than the communi- 

 cations and network fields. A bibliography covering other possible fields 

 of interest is given in an article by Murakami and Corrnigton. 



ACKNOWLEDGMENT 



The author is indebted to R. W. Hamming of the Mathematical Ke- 

 search Department w'ho supervised the computation of the seven place 

 tables, to Miss R. A. Weiss who planned, programmed, ran, and checked 

 the IBM computations of the tables and to Miss J. D. Goeltz who com- 

 puted the ten-figure accuracy check points required for the construction 

 of the tables. He also wishes to acknowledge the support and encourage- 

 ment given to the project by R. L. Dietzold and P. H. Richardson, and 

 the continued interest and helpful comments of B. A. Kingsbury. 



^ Kingsbury, B. A., private communication. 



'Murakami, T., and Corrington, M. S., Relation Between Amplitude and 

 Phase in Electrical Networks, R.C.A. Review, 9, pp. 602-631, Dec, 1948. 



