OF AIR AND OTHEE GASES. 5 



The ring and the tube are used in finding the moment of inertia of the 

 vibrating apparatus. 



The extent and duration of the vibrations are observed in the ordinary 

 way by means of a telescope, which shews the reflexion of a scale in the 

 mirror d. The scale is on a circular arc of six feet radius, concentric with the 

 axis of the instrument. The extremities of the scale correspond to an arc of 

 vibration of 19 36', and the divisions on the scale to 17. The readings are 

 usually taken to tenths of a division. 



Method of Observation. 



When the instrument was properly adjusted, a battery of magnets was 

 placed on a board below N, and reversed at proper intervals till the arc of 

 vibration extended slightly beyond the limits of the scale. The magnets were 

 then removed, and any accidental pendulous oscillations of the suspended disks 

 were checked by applying the hand to the suspension-tube. The barometer and 

 thermometer were then read off, and the observer took his seat at the telescope 

 and wrote down the extreme limits of each vibration as shewn by the numbers 

 on the scale. At intervals of five complete vibrations, the time of the transits 

 of the middle point of the scale was observed (see Table I.). When the ampli- 

 tude decreased rapidly, the observations were continued throughout the experi- 

 ment ; but when the decrement was small, the observer generally left the room 

 for an hour, or till the amplitude was so far reduced as to furnish the most 

 accurate results. 



In observing a quantity which decreases in a geometrical ratio in equal 

 times, the most accurate value of the rate of decrement will be deduced from a 

 comparison of the initial values with values which are to these in the ratio 

 of e to 1, where e = 2*71828, the base of the Napierian system of logarithms. 

 In practice, however, it is best to stop the experiment somewhat before the 

 vibrations are so much reduced, as the time required would be better spent in 

 beginning a new experiment. 



In reducing the observations, the sum of every five maxima and of the 

 consecutive five minima was taken, and the differences of these were written as 

 the terms of the series the decrement of which was to be found. 



In experiments where the law of decrement is uncertain, this rough method 

 is inapplicable, and Gauss's method must be applied ; but the series of amplitudes 



