490 Mr. T. Gray on Measurements of the Intensity of the 



taken from a watch with a centre seconds hand moving over 

 a dial divided to quarter-seconds. The watch was keeping 

 almost perfect time. In this case an observer counted the 

 oscillations of the magnet, and called now at the end of every 

 four or five periods, while the other observer noted the time. 

 Personal error does not enter into this method, as it is elimi- 

 nated in taking the differences. When the transits and time 

 were taken by the same observer, the time was taken from a 

 chronometer beating half-seconds. The observer took time, 

 say, at the beginning of a minute, and then counted the beats 

 until he could observe a transit. By simply counting the 

 number of beats between two successive transits, the total 

 number of periods in one minute could then be estimated ; and 

 the time of the first transit after each minute was then taken 

 as long as the amplitude was sufficiently large to allow the 

 time to be accurately estimated. Fractions of half seconds 

 were estimated from the position of the magnet at the beat 

 next before and next after transit. 



The results of the different observations of time were com- 

 bined in the following manner : — First suppose an even 

 number 2n observations to have been taken. The sum of the 

 intervals of time between the nth and the {n -f 1 )th, the (n — 1 )th 

 and the (n + 2)th, and so on to the 1st and 2nth, divided by 

 the square of the number of intervals, and by the number of 

 periods between each pair of observations, gives the average 

 period as nearly as it can be obtained from that set of obser- 

 vations. Suppose next an odd number 2n + 1 observations to 

 have been taken. The sum of the intervals between the 1st 

 and the (n + l)th, the 2nd and (n + 2)th, and so on to the nth 

 and (2n + l)th, each divided by the corresponding number of 

 periods, divided by the number of intervals, gives the average 

 period. Two sets of observations were usually taken ; and if 

 they agreed closely, the mean of the two was assumed to be 

 the true period. 



We have then the following equations for the determination 

 of H when one deflector only is used : — 



H 2r °' ( ) 



^ =(r? + a?) ¥ tan^ (5) 



o/ o . O 



F > (°) 



