68 



TABLES 35-36. 

 CYLINDRICAL HARMONICS OF OTH AND 1ST ORDERS. 



TABLE 35. 4-place Values for x 

 to 15.0. 



4.0 



TABLE 36. Roots. 



(a) ist 10 roots of JQ(X) =- o 



Higher roots may be calculated to better 

 than i part in 10,000 by the approximate 

 formula 



R m = R m _! + TT 



RI = 2.404826 



R 2 = 5.520078 



^3 = 8.653728 



R* = 11.791534 

 R 6 = 14.930918 

 R 6 = 18.071064 



J?7 = 21 . 2II637 



R & = 24.352472 



Rg = 27.493479 



Rw = 30 . 634606 

 (b) ist 15 roots of Ji(x) = = o 



dx 



with corresponding values of maximum or 

 or minimum values of Jc(x). 



Higher roots may be obtained as under (a). 

 NOTES, y = J n (x) is a particular solu- 

 tion of BessePs equation, 



The general formula for J n (x) is 

 ^_(-i)^- Mto 

 o 



or 



when is an integer and 



T fv\ 2H T ( 

 J n+l\XJ J n \- 



and 7 T / \ 



SMITHSONIAN TABLES 



^ ' 



J_ n (^)=(-l)/nW. 



Tables 35 to 36 are based upon Gray and 

 Matthews' reprints from Dr. Meissel's 

 tables. See also Reports of British Associa- 

 tion, 1907-1916. 



