162 



On the Motion of Vibrating Bodies. 



[Apr. 19, 



of the object-glass o£ a telescope the observations can be made from a 

 considerable distance ; this may be useful when a shaft in an inaccessible 

 situation is the subject of experiment. 



It seemed advisable to determine the effect of alterations of temperature 

 on the period of the fork, which might be so great as to render some cor- 

 rection necessary. Eor this purpose two equal forks provided with 

 mirrors, and making about 60 vibrations a second, were enclosed in 

 wooden boxes containing thermometers, which were placed between the 

 prongs. One of the forks was fixed in a vertical position and the other 

 horizontally, the box containing the latter having its lower side replaced 

 by two pieces of sheet zinc, separated by a layer of air about half an inch 

 in thickness. By the flame of a small gas-burner the temperature of the 

 air in the box could be raised to about 60° C. At the side of each box 

 was a hole opposite to the mirror, and closed by a plate of glass. The 

 Lissajous' figure obtained by the reflection of a point of light in the two 

 mirrors was observed in a small telescope ; and the time required for the 

 passage of the figure through a whole cycle was determined when the 

 thermometers indicated different temperatures. There was some doubt 

 whether the thermometers gave a true indication of the temperatures of 

 the forks ; but in the series of experiments giving the most concordant 

 results the heat was applied near one end of the box, and at the greatest 

 possible distance from the thermometer, in order to set up convection 

 currents to equalize the temperature of the air and fork as completely as 

 possible. It would be no doubt preferable to introduce into each box a 

 small fan to keep the air in continuous motion ; in all cases the tem- 

 perature was changed very slowly, and a considerable time allowed to 

 elapse between two observations. In the last series of nine observations 

 the differences between the temperatures of the two forks varied from 

 9° to 27° C, and from the observed results the increase of the period of 

 the heated fork for 1° C. was calculated. The mean loss per minute for 

 1° C. amounted to *4013 vibration in 3600 ; the minimum number being 

 •3921, and the maximum -4043. That is to say, a fork giving 3600 vibra- 

 tions a minute at the ordinary temperature, would give 3599*6 when the 

 temperature is raised 1° — a loss of about -011 per cent. So that if a 

 determination of velocity were made at a temperature 20° above that at 

 which the fork is giving exactly 3600 vibrations per minute, a correction 

 of '22 per cent, would have to be deducted from the number obtained. 



There is some difficulty in determining the exact number of vibrations 

 of a large fork ; the difficulty, however, disappears when a graduated 

 cylinder or disk is driven with a constant velocity, and the number of 

 vibrations per second calculated from the form of the figure produced by 

 the fork. This method has been employed with the forks at present in 

 use, and by proper arrangements it can be applied to the determination 

 of the numbers of vibrations produced by musical forks ; but up to the 

 present we have failed in producing by means of clock-work a rotation 



