C. S. Peiree—On a Method of swinging Pendulums. 115 
There would be no insuperable difficulty in making the pen- 
dulums so near alike that y should be less than y, even if the 
latter quantity were smaller than it would be likely to be. 
But it will be seen presently that care must be taken in the 
construction not to make y too small. + 
We shall have then dl<y or z<1; Sets aces 
period of the first terms is shorter than 
that of the second terms. From this it 
can be shown to follow that the whole = 
oscillations of the two pendulums have | i-46-@------O Pa 
the same period, which is that of the ~ 7 : 
harmonic motions represented by the first terms of their values. 
Thus, in the figure, the abscissas representing the time, we 
have a wave of short period and large amplitude placed in com- 
parison with a wave of long period and small amplitude. 
The phase of the short wave advances on the long one and 
goes over and over it. In each complete eycle of the curve 
representing the short wave, beginning and ending at y=0, it 
must cut the other curve twice unless the latter has mean time 
crossed the axis of abscissas once and not twice. When this hap- 
tes PERRET Ee 
ol)? 
Now let us suppose that dl is so small that 4 ae may be neg- 
lected, being less than one millionth. This would happen, for 
instance, if 5 were one meter, y a half a millimeter (so that the 
stand would be somewhat less stiff than the Repsold tri : 
and &/ were one twenty-fifth of a millimeter, so that the dif 
ference between the natural times of oscillation of the two pen- 
