ESTIMATION OF SMALL EXCESSES OF WEIGHT. 27 



To measure 6. — The angle of deflection was measured by 

 the number of divisions of the scale which the pointer 

 moved over. As the length of the pointer is 32*1006 cen- 

 timetres, while 20 divisions of the scale measure 2*5658 

 centimetres, a tenth of a division, in terms of which the 

 deflexion was measured, corresponds to an angle of 

 0*0003996°. The oscillations were observed from a distance 

 of six or eight feet by a telescope. The resting-point {i. e. 

 the point where the balance would be in equilibrium) was 

 found in the usual way by observing three successive 

 extremities of two swings and taking the mean of the 

 second and the mean of the first and third. Five deter- 

 minations of the resting-point were usually made with the 

 excess to be measured alternately added and removed. 

 From these five, three values of the deflection {n) due to 

 the excess were calculated in a manner which will be seen 

 from the example below. 



7'he Time of Vibration. — This was found from several 

 determinations of the time often oscillations. The method 

 will be seen from the example. No correction was needed 

 for the resistance of the air as long as the vibrations did 

 not exceed two divisions of the scale. When, however, 

 they were much more than that, the time of vibration was 

 found to increase with the arc. As the time of vibration 

 frequently changes slightly, probably through variations 

 of temperature, it was usually observed before and after 

 the determination of the deflection {n) and the mean of the 

 two taken as the true time. 



The following example of the determination of the value 

 of a centigramme rider by placing it halfway along the 

 beam will sufiiciently explain the details of the method. 



