92 BELL SYSTEM TECHNICAL JOURNAL 



Arrays of Arrays 



Each element of a generalized linear array, such as shown in Fig. 21, 

 may be replaced by a generalized array, thereby producing an array 

 of arrays.^ It may be shown that the resultant is given by an array 

 factor, representing the characteristics of individual arrays, times 

 other factors representing the relative position of the individual arrays 

 in the array of arrays. A derivation analogous to that beginning on 

 page 22 results in the equation 



_ sin n'lria' sin + b') 



K = T 



n' sin 7r(a' sin (/> + h') 



sin N'r{A' ^\n + B') sin N'-k{A' sin </> + B') 

 ' N' sin Tr{A' sin + iJ') ' N' sin Tr{A' sin + 5') ' 



(35) 



where a'\, A'X and A'\ are the coordinate spacings between arrays and 

 b'T, B'T, and B'T are the corresponding phase intervals, and r repre- 

 sents the characteristics of one of the individual arrays. If each array 

 is of the type shown in Fig. 5, r is given by equation (14) above. 

 Placing n' = N' = 1 and N' = 2 also n = 2 and B = 0, the above 

 equation reduces to 



sin A^'7r(yl'sin<^ + 5') sin 7V7r(^ sin 0) t ,, , .-,, 



-K = -T77— : \ A , ■ , ^,\ ' TT—- T—A — = : COS -r (1 — COS (b), (36) 



iV'sm7r(yl'sm<^ + j5') iVsm 7r(^ sin0) 4 ^j^ \ j 



which is that made use of in calculating the diagrams in Figs. 14 and 15. 



Bibliography 



Sources with extensive bibliographies: 



Walter, L. H., "Directive wireless telegraphy," 119-121, 1921. 



Beverage, H. H., Rice, C. W., and Kellogg, E. W., "The wave antenna," Trans. 



A. I. E. £., 42, 215-266; February, 1923. 

 Zenneck, J. and Rukop, H,, "Drahtlose Telegraphie," 486-508, 1925. 

 Smith-Rose, R. L., "A study of radio direction finding," Radio Research Board 



Special Rept. No. 5, 1927. 

 Keen, R., "Wireless direction finding and directional reception," 451-467, 1927 



(2d Edition). 

 Smith- Rose, R. L., "Radio direction finding by transmission and reception," Proc. 



I. R. E. 17, 425-478; March, 1929. 



1926 



Bellini, E., "La possibilite de la telegraphic sans fil dirigee a grande concentration," 



L'0?J(fe £/ec/., 5, 475-483; September, 1926. 

 Bontsch-Bruewitsch von M. A., "Die Strahlung der Komplizierten Rechtwinkeligen 



Antennen mit Gleichbeschaffenen Vibratoren," Ann. d. Physik, 81, 425-453; 



October 18, 1926. 

 Catterson-Smith, J., "The characteristics of beam transmitting aerials," Jour. 



Indian Inst. Sci., 9B Part 2, 9-19, 1926. 

 Chireix, H., "Transmission en ondes courtes," L'Onde Elect., 5, 237-262; June, 



1926. 



•Bailey, Dean, and Wintringham, Proc. I. R. E., 16, 1694; December, 1928. 



