"' — 1 ^h ' 



( 812 ) 



(lil- b =: O, 'Jlv {) =: 0. 



Ö!)- O'),, 1 /f) d\ 1 



ö!), d\), 1 /d ö\ 1 



^ — == — - — - ,(■ ^ \ b J o n,, . 



dz d.r r \df (IcJ ■' ^ e ^ ' 



dl)y d.h- 1 /ö ö\ ^ , 1 



d.v (},/ ,■ \dt d.rj c 



èy öxT t' \J)t d.i 



db^. dö, _ 1 /d ö 



d~ d.v c \dt d.c 



d.v oif c \dt o.cj 



L = bx H ('•*/ b~. — ". 5,/ ), 



c 



L = b. »• ih -I (lu (u- — u^ (), ), 



^ ^ C' c 



f, = b,- -I /r f)„ H (U:, f),/ — it^ f). ). 



c c 



§ 4. We shall further transform these formulae by a change of 

 variables. Putting 



--— = P (3) 



c — tv 



and understanding by / another iiumerit-al (juantity, to be deter- 

 mined further oji, I take as neNv independent \ariables 



.r' = k I .V , ij' — hi , :' — I z (4) 



/ w 

 t' — ^t — hi X (o) 



/• .;' ■ 



and I detine two new vectors b' and I)' l»y the formulae 



b'. = i b, . b, = ;^ f b, -';;-(). \ b', = U^~.^ ~ o. \ 



1 /■ / ir \ , k / a 



^fv, I)V-,-U,v+~^. . fV^-T^U) 



for which, on account of (3), we may also write 



b, -= i^ b', , b, = kl^ U', + '-^ I)'.- \ b, = /• l^ j^b', - '"-^ h'y jl 



()^ = /-^ ./, , [)^ ^ kl^ f\)'y - ^ b', \ (), = X- 1^ U', + ^b' 



(0) 



