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C7 rx’, ee 
, \ ‘ fe sin(e-+-¢s,;—ha) (21) 
fost of” anette, 
gZyh,t 
that is, nearly, if a be considerably different from ea 
c., ht =1x* 11 CO8(Ey + ts\, — Kx) 
eo 21y 
dk . ( 
a sisi (toe — #4) ' 
We have therefore the approximate expressions : 
Sot = 1A yr COS (€, + 8, — Fe), if <i 3 (22) 
and 
Byes 0 anes «2; 22)’ 
Boies” Bie dk’ ( ) 
we have also nearly, in general, 
Sekt = 3 x AY 7,1 ©O8 ( + ts 17 Fx), if x ah ri (22)" 
but the discussion of the case when 2 is nearly = (Pris too 
long to be cited here. The formula (22) for g. h, ¢ Com 
cides with the particular integral (4)‘; and the condition 
_ which it involves with respect to 2, expresses the law ac- 
cording to which this particular integral comes to be 
i true for greater and greater positive values of x and 
t, ar *>0,) after having been true only for negative values 
dk 
of x when ¢ was = 0, 
In the particular case » = 3, the foregoing formule 
have an immediate dynamical application, and correspond 
to the propagation of vibratory motion through a system of 
mutually attracting or repelling particles ; and they conduct 
