derived from M. Cauchy’s Theory. 207 
Between these it is possible to eliminate the three medium-con- 
stants a) a, @., and thus to deduce a general relation, valid 
for all media, between the four indices ph, Hp Hp My» and the 
four periodic times tz tp Tp Ty. 
Now, a little consideration will show that this relation can 
only involve the two ratios of the three differences of the four 
indices, and the two ratios of the three differences of the four 
reciprocals of the squares of the periodic times. Taking 
these we may for abridgement write, 
Py —& = 
PESOS BY Sag? VE RIEL Be Sp (14.) 
Profs Pu Ps 
ciate lage 7 Bt a i penile A (15.) 
Paeitg, May ar ig re 
Then it will appear that the result of elimination will be a 
relation between the four quantities s, sp tp tp only; and will 
not involve the four other quantities hp, My Ty Ty if we pre- 
viously substitute for #4 wp tp’ rp” their respective expres- 
sions deduced from (14.) and (15.), which are 
Hp = Pp +Sp Hu—Ps) I 
Hp = Hy + Sp (Hyp) 
oe? =\t9° + ty (a 75°) ; 
ta = ahs at (7H —T3°) 
(16.) 
(17) 
This result of elimination will therefore be the same as if in 
the equations (13.) we had supposed 
4 
to 
II 
™~ 
D ie ts ie (18.) 
ae pe be. =. tp 
ols Oieatia =e Ola iG,| J 
that is, the same as if we eliminated any two new quantities 
b and c between the three new equations 
Sm = btp + ¢t,* 
: (19.) 
“a 
7" 
Il 
~ 
= 
= 
a 
™~ 
