NO. 7.] HORIZONTAL INTENSITY. 67 



OBSERVATIONS OF VIBRATION. 



The vibration-box belonging to the apparatus is furnished with suspension- 

 tube and cocoon-thread, by which each of the two magnets, V and VI, may 

 be suspended. The magnets have pointed ends, and the vibrations are ob- 

 served with the naked eye. For the reading of the amplitudes, two different 

 scales are placed at the bottom of the box, one a circle division, by the aid 

 of which degrees and fractions of degrees may be read off directly, and the 

 other a linear scale, of which the advantage is that the division-marks are 

 farther apart. On this account, the latter scale was constantly employed. 

 By a series of measurements taken in Hamburg, June 6th, 1893, one scale- 

 division was found to equal 1'91 mm., and as the length of the magnets V 

 and VI is respectively 99'0 mm. and 98'0 mm., the arc-value of one division 

 on the linear scale is respectively 2'21 and 2'23, mean 2'22. 



The way in which the vibration observations were made was that the 

 time was noted to tenths of a second every third time the point of the 

 magnet passed the middle division of the scale (zero) from the 1st passage 

 to the 31st inclusive, and subsequently from the 101st to the 131st inclusive. 

 Immediately before and after each series of vibrations, the magnitude of the 

 amplitude to each side was read off on the scale to tenths of a division, 

 with the hour belonging to it; while at the same time the temperature was 

 read off on the thermometer placed with its bulb in the vibration-box. If 

 the time of vibration directly deduced from each series of vibrations is called 

 T', we obtain the actual time of vibration, T, from the formula 



logT=log2" logy + log?, 



where y is the correction for arc of vibration, and Q is the correction for 

 rate of chronometer, the sign -f- being used when the chronometer loses, 

 the sign -- when it gains. 



I have calculated y by the formula 



y = 



[2- 



where h and h^ indicate the amplitude of the needle from the middle 

 division in scale divisions, respectively for the beginning of the vibration 



