14 
DETERMINATION OF THE RATE OF VIBRATION OF TUNING-FORKS. 
Method of comparing tivo forks. 
Two forks, the vibration numbers of which differ very slightly from one another, 
may be conveniently compared by the method previously mentioned, namely, by 
placing them at right angles with one another, and in such positions that the images 
of their edges are seen to cross one another in the field of view of the microscope. 
When the forks are vibrating, a modification of Lissajous’ figure is seen in the angle 
made by the two images. If the forks are nearly of the same pitch, the corresponding 
Lissajous' figure, obtained in the usual way, is, as is well known, a straight line 
changing to an ellipse which passes into a circle, then to another ellipse, and finally 
to another straight line inclined the opposite way to the first. When such a pair of 
forks, nearly in unison, is under observation, one of the lines is represented by a bright 
line bisecting the angle (due apparently to a diffraction phenomenon at the edge of 
each fork) ; this line then becomes double, and changes into an ellipse and finally 
to a circle. Directly the change from the line commences, the angle between the forks 
becomes filled by a dark shadow. The circle appears surrounded by a bright line, but 
the second ellipse is bounded on one side by a dark shadow, and on the other side by 
a bright line. At that part of the figure corresponding to the line lying across the 
angle, the angle itself appears to be filled up by a dark shadow with a well-defined 
edge. The figure then passes through the changes in the reverse order. The instant 
when the angle is free from shadow is very sharply defined, and, starting from this 
point, it is quite easy to count the number of optical beats which take place in a given 
time. The two forks may be kept in vibration by careful bowing, an assistant being- 
required to bow the horizontal fork. 
With two forks, one the octave of the other, the parabola seems to rest like a dark 
shadow alternately on the two forks. At these instants the angle is free from shadow , 
the figure of 8 is also perceptible surrounded by a bright line. 
We found that the fifth could also be compared in a similar manner, but the obser¬ 
vation was not quite so easy. In this case the sharpest indication was the filling up 
of the angle by shadow. With more complex relations between the two forks no 
sufficiently visible phenomena were perceptible. 
Although, undoubtedly, great accuracy may be attained in counting beats by the 
ear, in some respects the optical method is more serviceable ; it also permits of an 
extended observation, as the forks may be bowed without altering their phase. 
As the question of absolute pitch has recently attracted much attention, and as 
tuning-forks are becoming more and more employed for measuring small intervals of 
time, we hope that the experiments above described may prove a useful contribution 
to the knowledge of the subject. 
