M7 

 tliat is, nearly, if a? be considerably different from t-rrrt 



(21) 



(21)' 



g,7i,t ~ 1 h,l \ 1 ' 1 / 



We have therefore the approximate expressions : 



%,„.. = ^V\, <^°' (S + '* 1 - ^'-)' 'f- <'§^; (22) 

 and 



iM = 0'''^->#' (22)' 



we have also nearly, in general, 



%, ,, t = i ^\ '\a «°^ (s + *'\ - f''^)' "f ^ = ' § 5 (^^y 



but the discussion of the case when .r is nearly zz:t-~'is too 

 long to be cited here. The formula (22) for S . coin- 

 cides with the particular integral (4)'; and the condition 

 which it involves with respect to Xj expresses the law ac- 

 cording to which this particular integral comes to be 

 (nearly) true for greater and greater positive values of x and 



t, (if -77^ >0,) after having been true only for negative values 



Cln 



of X when t was = 0. 



In the particular case n ^ 3, the foregoing formulae 

 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 



