114. C.S& Peirce—On a Method of swinging Pendulums. 
We may also consider the parts of the stand on which the 
a Pea rest as equally elastic. We may therefore take 
s ) as proportional to 4(g,+9,), and is, ane as pro- 
Social to $(9,—¢2). Denoting, then, by x and y two 
constants sae values will be easily détermitnble by experi- 
ments we hav 
8,+8, geek! (P,+ ,) 
(2@—Y) (P,—P,) ; 
or 8, =LP,+YP, 
8,==LD,+YP, 
Substitutin ng these values of s, and s, in the differential 
“seb a and also writing +01 for 1, and 7—al for l,, they 
& 
(-+a+ 61) 2 + yER=— 9 9, 
Ps 
(/-+-2— 61) sat y ae =—9P,. 
The solution of these equations is i B, ¢,, and ¢, being the 
arbitrary constants) 
iss REG OUP Jo. 50 { | g t 
pane) | (1) ane] | (¢ t) 
cestlgl katt) 
Ws a(S Ja +(F) onl a ied 
OE: dl\? g Suk eS 
mee F — ) oo = Vanry ot 
The condition that the pendulums are started by drawing 
them away from their positions of equilibrium and then letting 
them escape nearly at the same instant makes t, and ¢, nearly 
equal. We may reckon the time from the mean instant of 
Peas, Ove ee that instant we have very nearly 
rane @))-H( Ja) 
or if we write z for © batted 
P=—A (e+/1F2) — B (e—-/1+2). : 
And since the amplitudes are nearly equal and the phases 
nearly o * eae 
or Arba B= = (ty) A (24 142)+ B (e—/T 2) 
8 
“ 
: — nearl gi OO 7 
z : 2 ae 
