40 



Mr. L. C. Jackson on the Theory oj the 



Returning to equation (7), we find that the damping 

 coefficients q, r, and s have the following values : 



2 /R 1 L 2 4-L 1 R 2 . R2L3 + L2R3 RsLx + LaRj PRP \ 



_ffli v — cr ~ + — c; — + - ~cr - +r i r » e «; 



- aVCRjLjLs + LAU + Li'LjB, - R a M 23 2 - B 2 M 18 S -R 3 M 12 2 )] 



-T 2 (fi) 1 2 ft) 2 2 — ft» 2 2 ft) 3 2 + Q)3 2 <wi 2 — «i 4 ), 



LC2C3 G1C3 Ci0 2 



9 /R 1 L 2 + L 1 R 2 R 2 L 3 4-L 2 R 3 -RsLi + LsRi . -p -p -r \ 



- C0 2 -I ^ 1 ™ 1 ^ 1- iii^Ka I 



- o) 2 4 (R 1 L 2 L 3 + LAI* -r L X L 2 R 3 -R* 2 - R 2 M 31 2 - R 3 M 12 2 ) ] 



-f- 2 (C0 1 2 C0 2 2 + W 2 2 0)3 2 — C03 2 ft)l 2 — ft> 2 4 ), 



LC2C3 C1C3 CiC 2 





-0.3 2 ( 



RxLa + LA , B 2 L 3 + L 2 R 3 , RsLi + LsRi 



+ 



+ 



+ R 



^R^J 



Cs Ci c 2 



- co 3 4 (R 1 L 2 L 3 + L 1 R 2 L 3 + LxLjRb-RiMm'-IIjM^-RbMu*)] 



-~ 2( — &)! 2 ft)2 2 + ft) 2 2 &) 3 2 + Ws 2 ^! 2 — &) 3 4 ) . 



By means of the previously used abbreviations, the values 

 of q, r, and s can be written in the following form : 



q = [lym 2 n 2 + k 2 n 2 l 2 + hl 2 m 2 -o) 1 2 {n 2 (^ 1 + ^) + Z*(*, + jfe 8 ) + m 2 (£ 3 + £ 1 ) -> 



+ *i*A } - *>i 4 (£i + £2 + ^3 - Z^/3 2 - Ayy 2 - £ 3 « 2 )] 



-r2L 1 L 2 L 3 (<»l 2 &) 2 2 — ft> 2 2 ft> 3 2 + G) 3 2 G)i 2 — ^i 4 ), 



r = [k im V + k 2 n 2 P + k 5 lV- <o*{n\h + *.) + / 2 (* 2 + h) + m\k> + h) 



+ kihh} - w 2 \k x + h 2 + k 3 - J^/3 2 - k 2 y 2 - £ 3 a 2 ) ] j, (10) 



-T- 2L 1 L 2 L 3 (co 2 co 2 2 + co 2 ' 2 co 3 2 — (oz 2 ay l 2 — co 2 4 ), 



5 = [^mV + ^ 2 / 2 4-/^ 2 m 2 - W 3 2 {n 2 (A- 1 + ^) + Z 2 (* 2 + £ 3 ) + m 2 (* 3 + jy 

 + MA} - <*>s\h + k 2 + h-Jc^ 2 - k 2 y 2 - £ 3 a 2 )] 



-=- 2L 1 L 2 L3 ( — W 2 C0 2 2 + ft) 2 2 ft) 3 2 + CDS 1 '(Di 2 — G) 3 4 ). J 



