34 MEASUREMENT OF OSCILLATIONS. 



In order to investigate this motion, we observe either the passage 

 of an index in front of a divided scale, or the image of a line on a 

 micrometer in the focus of a telescope, or the image of a division on 

 the cross-wire of the telescope, whether this division has been traced 

 on the movable system, or whether it arises from the reflection of a 

 scale in a mirror. In all cases there should be a means of noting 

 the passage of the system through a definite position, and of 

 estimating the angles of deflection. 



The time of an elongation could not be determined with exacti- 

 tude owing to the appreciable time in which the movable body is 

 in apparent rest ; we can, on the contrary, exactly determine the 

 time at which the movable body passes through any given position 

 in the region in which its velocity is greatest that is to say, near the 

 position of equilibrium. 



Whatever be the position which serves as marks, the difference 

 between the time of the two successive passages in the same direction 

 represents exactly twice the time of what is ordinarily called a single 

 oscillation. 



In order to get this time accurately, it ought to be deduced from 

 a great number of transits. When the oscillations are maintained for 

 a very long time, like those of the pendulum, Borda's method of 

 coincidences enables us to solve the problem with all the accuracy 

 desirable ; but this method would lend itself with difficulty to the 

 observations we have here in view. And, moreover, the mode of 

 observing would not be the same according as the damping is more 

 or less rapid. 



690. If the motion can be observed for some time (a quarter of 

 an hour, for instance), we may determine the time of oscillation as 

 follows : 



Let us assume, as is the case with a magnetised needle, that the 

 time of the oscillation is from 3 to 5 seconds, and that the divisions 

 of a scale pass the cross-wire of a telescope. A division near the 

 centre of the amplitude is taken as mark that is to say, near that 

 which corresponds to equilibrium. By means of a counter, the time 

 / is noted at which this division passes over the wire in a certain 

 direction, either from right or left this is the initial passage of order 

 zero ; the successive vibrations are then counted, and the time t l of 

 the 2oth transit, which is in the same direction as the first. At 

 the same time the extreme divisions, corresponding to the initial 

 vibrations, and those of the 2oth are observed, from which are de- 

 duced the corresponding angles of deflection a and a r It is 

 unnecessary to count the following vibrations, for we know that the 



