204 



Dr. J. R. Airey on Bessel Funch 



the values to about four places of decimals, e. g. <r 2 of 

 J' (V) = is 3*4183, the correct value to five places from 



the ascending series being 3*41839. 















n. 



d=a- i / sJ2n. 



(T 2 . 



71. 



c = oJ V2?i. 



(T 2 . 



1 

 2 ■ 



.. 0-7717 



2-9751 



. 



.. 1-0000 



3-8317 





0-7859 



30212 





1-0093 



3-8718 : 





0-7997 



30669 





1-0184: 



3-9117: 





0-8131 : 



31 121 : 





10275 



3-9515 : 





0-8262 



31570 





1-0364 • 



3-9911 



-I • 



.. 0-8389 : 



3-2014 



1 



8 • 



.. 1-0452: 



4-0305 





0-8513: 



3-2455 





1-0539: 



4-0697 : 





0-8634 



3-2892 





1-0625 



4-1088 : 





0-8752 : 



3-3326 





10710 



4-1477 : 





0-8867 : 



33756 : 





1-0793 : 



4-1865 : 



4 • 



.. 0-8980 



3-4184 



i ■ 



.. 1-0876 



4-2251 : 





0-9090 : 



3-4608 : 





1-0958 



4-2636 : 





09199 



3-5030 : 





1-1038: 



4-3020 





0-9305 : 



3-5449 : 





1-1118: 



4-3402 





09410 



3-5866 





1-1198 



4-3783 



1 



— 8 • 



.. 9512 



3-6280 



6 • 



.. 1-1276 



4-4162 : 





0-9613 



3-6692 





1-1353: 



4-4541 





09712 



3-7101: 





1-1430 



4-4918 





0-9809 : 



3-7508 : 





1-1506 



4-5294 





0-9905 



3-7914 





1-1581 



4-5668 : 



. 



.. 1-0000 



3-8317 



1 



.. 11655: 



4-6042 



Roots of -j- m .ZP:Jp(z). 



If a long deep beam is supported at its ends and prevented 



from turning- about its axis and loaded with a single trans- 

 . . . .... 



verse load at its middle point, the condition of critical 



d /x' 2 \ 



stability is determined by the roots of j-.pJil^ I and 



for a beam with uniform load, by the roots of — . x^Ji ( -» J. 

 Taking the general case, to find the roots of 

 d 



dx 



X*J p (2px2p)=r- 0, 



(5) 



where p has been written for - — h , change the variable by 



r z \*P m + 2 



substituting x — ( «— J ; then (5) becomes 



