Vibrations : Both Masses and Periods Unequal. 

 Equations (27) and (28) in (25) give 



/■=B + F, 



and 



w h 



ence 



and 



rhere 



Pf _ ,_ a ->/{( a - c )2 + 4p6 2 } E 

 l+/3~ 2b 



c _ q+i/{(a-c) 2 + 4p6 2 } ir 



+ ~ 2b ' 



F (_ c + a + S)(l+/3) + 2&/3' * ' 



a_ 4 /0 6 2 (l + £) + 2&ft(c-a-S) 



H~ 4p/> 2 (l + /3)+26/3(c-a + o)' " 



S s =(c-a) 2 + 4p6 2 



41 



(29) 



(30) 



(31) 



(32) 

 (33) 



These give the values of the ratios o£ the constants deter- 

 mined by the initial conditions in question, and this is all 

 that we need to check the records experimentally obtained. 



II L Experimental Results. 



Masses 20 : 1, Lengths 4 : 3 (?; = 3 : 4). — The relations were 

 calculated from the theory given so as to obtain any desired 

 values of the coupling and frequencies, the results are shown 

 in Table I. For the longer pendulum the sum of pendulum 

 length and droop of bridle was 229 cm., and it had the 

 heavier bob. 



Table I.— Masses 20 : 1, Lengths 4 : 3 (*?=3 : 4). 



Coupling 

 =7- 



Bridle Droop 



— R 



Frequency 

 Ratio 

 p:q. 



—P 

 Long Pendulum Length. 



Per cent. 







4-245 



9-96 

 17-07 

 28 

 34-43 







0-2 

 05 

 1 



2-12 

 3 



1154 

 1-255 

 1-403 

 1-62 



2 

 2-29 



Figures 1-5 (PL II.) show photographic reproductions of 

 the double sand-traces simultaneously obtained, with masses 

 20 : 1, t. e., p =20 and the length of the pendulum carrying 

 the lighter bob 3 : 4 of that with the heavier bob. The first 



