30 



Prof. Barton and Miss Browning on 



case is now reduced to a static one. Thus., for the present 

 case, equation (12) becomes 



w — ( a — c){xoc(a — b) + (y + z Q )(2ab — bc — ca)} .^ 

 a{4:ab—'6bc — ca) 



Whence 



_ _ (a — b)(a — c)x 

 y«- z *- w *- a - + ?,ab-2be-2ca- 



(36) 



We may thus represent the present initial case mathe 

 matically as follows : — 

 For t = 0, 



_ (a — b)(a — c)x _ ^ 



)5 y ~ a(b-c) + (a + 2bXa-c)~ Z > I 



x ~ X , 



dx dy 



dt U ' dt ' 



dz 

 dt 



(37) 



= 0. 



Then equations (37), substituted in the general equations 

 (30), lead to 



a(b — c) — 3b(a—c) 



i? 1= 0, 



A.= * 



3a{b-c) + {a-i-2b)(a — c) 



*o, 



. _ da(b — c) + 3(a + U )(a-c ) y , 



Ad ~ Z{a(b-c)~+(a + 26) (a-c)}^ 



<*i 



0, 



IT 



~2' 



77 



This set of equations is like the set (33) except that A 2 

 and A 3 are different fractions of a? . 



It is accordingly scarcely necessary to write for this case 

 a set of equations like (34), the solution being given by (30) 

 and (38). 



Case 111. — Let the pendulum bob Q be pulled aside and 

 held displaced y=y till the other bobs P and P are hanging 

 freely at rest in equilibrium ; then Q is let go. It is then 

 obvious that the displacements x and z Q of the bobs P and P 

 will be calculable functions of y and the constants involved 

 in the systems. But these functions are somewhat cumbrous, 

 and their exact values are not needed for a general examina- 

 tion of the resultant vibrations which occur "*. Thus we may 



* In any actual experimental case .r and z Q could be measured for a 

 given y and their values inserted in (40). 



