C. S Peirce—On a Method of swinging Pendulums. 117 
of the observed periods would not be the same as the mean of 
the periods of a cycle. 
The quickest oscillation of either pendulum would occur 
when the phases of the component harmonic motions were 
coincident, the slowest when these phases were opposed. The 
period of the slow harmonic component motion would be 
L+-e+y 
g 
or the mean of the periods of the two given pendulums oscil- 
lating on the given stand with coincident phases, so as to be 
affected by the flexibility of the whole stand but not by its 
liability to distortion. Suppose, then, that in the course of 
the experiment an instant comes at which the pendulums are 
vertical at once. Let us reckon the time from this instant, 
and put 
1-2 Pept? 
ae SY V7i+g—-1—2 
so that I is nearly unity. Then using the abbreviations 
sin, = sio} | Go .t 
L+a—a/(d1)"--y 
sin, =sin| | ef 
we have 
C gp, = (W142 41—2) sin, + I (V1 +2'—1+-2) sin, 
C gp, = (-W1 42 -1—2) sin, +I (—V1 +2°+1+2) sin,, 
where the double sign distinguishes between coincidence and 
opposition of the phases of the harmonic constituents at the 
zero of ¢. ; 
Then since the value of z is between 0 and unity, the values 
of these four coefficients lie 
/j} +2 +1—z between 2 and 1°414 
Vi +f—1+2 ores 
—/142—1-z —% . S414 
—V ji 4274142 a 0°586 
quickest, and vice versa. Then from the symmetrical character 
of harmonic motion it follows that if observations were taken of — 
