of Edinburgh, Session 1871-72. 
673 
conclude that k, k,... are constants. [They are sometimes called 
the “cyclic constants (Y. M. §§ 62... 64)]. The equations of motion 
(15) thus become simply 
dio , $PQ , 
dt 
. f /da 
k {t 9 
-SH 
e da! d/3\ ) 
K dp dif/ J S 
+ 
«{■(» 
- 4 ) + k '( 
'da' dj3'\ j 
.35""#) + "4 
+ 
&c. 
II 
* 
1 
• 
..(16), 
with corresponding equations for 
7] 0 , £ 0 , and with the following 
relations from (7), between £ 0 , iy 0 ... 
and if/, p, ,m * 
dQ 
, dQ 
. dQ , . 
(17). 
d$o 
n dv o ~ dL~ 6 ’ &c ■ ‘ 
7. Let 
/ da d/3^ 
v / da' 
df3'\ 
\d<p dif/ j 
1 + k \t 9 ~ 
be denoted by {<p, if/} . 
(18), 
so that we have 
x l'}= ~ 
{ 4’, 9} • 
(19). 
These quantities {<£>, , { 0, if/} , &c., linear functions of the cyclic 
constants, with coefficients depending on the configuration of the 
sj^stem, are to he generally regarded simply as given functions of 
the co-ordinates if/, <p, 0, ...: and the equations of motion are 
In these (being of the Hamiltonian form) Q is regarded as a 
quadratic function of £ 0 , rj 0j £„••• with its coefficients functions of 
if/, <p, 0 , &c.; and J) applied to it indicates variations of these co¬ 
efficients. If now we eliminate £ 0 , rj 0 , £ 0 *** from Q by the linear 
equations, of which (17) is an abbreviated expression, and so 
have Q expressed as a quadratic function of ij/, <p, $,*•• , with 
its coefficients functions of if/, <p, 6, &c .; and if we denote by 
dQ 
dp' 
dQ 
dif/ 
&c., variations of Q depending on variations of these co- 
