Johnston — Initial Motion. 



19 



In these equations we are to regard asu, a^, &c., as the values of 

 these quantities when the initial values of the co-ordinates are intro- 

 duced, and t taken = 0. 



We now have 



«1J 5^2 



h + an 5^2 + + dm 56,, = ( 0i - -^ 1 5<, 



/ db2\ 



+ ail IQi + ai, n 50,, - 1 ®2 - -^ 1 5^ 



/ dbn.A 



ai,n+l50i + fl2, m+l 502 + «», m+1 50,i = ( 0n+l + *1 "TT" ) ^^• 



The first m of these equations give, at once, the initial motion, and, 

 by combining the first n with each of the last m equations, we get the 

 initial reactions. For instance, $1 is given by 



«n «i2 



«12 «22 



«ln «2n 



«ln 

 «2n 



an an 



an «22 



am a2!» 



dbi 



am 



©1 



dt 



«2.. 



02 



dbi 

 ~~di 



db„ 



• ann ©n y~ 



at 



a\ n+\ ajn+l • • • a») h+1, ©n+l — 



dbn 



dt 



= 0. 



C 2 



