118 



/ — T and / 4- T, It will be seen at once, on substitution, 



that 



e, 4- -29 + 6' =0. 



Hence by combining the three readings according to the 

 preceding formula, the deviation of the magnet from its 

 mean position, arising from the vibratory movement, is com- 

 pletely eliminated; and it will readily appear that the same 

 result may be attained by any greater number of readings, 

 taken and combined according to the same law. 



Now, let the value of 9 contain an additional term, 4"i^^ 

 proportional to the time : or, in other words, let us suppose 

 that there is a progressive change of the declination, which 

 may be regarded as tmifarm during the whole interval of 

 observation. It is then manifest that 9^ + 29 + 9' — 4pt ; 

 and accordingly that the quantity 



\{B, + 29-\-9') ' 



will give the mean place of the magnet corresponding to the 

 epoch t. 



The supposition of a uniform change can, however, be 

 regarded as an approximation to the truth, only when the 

 interval of time between the first and last reading is very 

 small, in comparison with the interval between the successive 

 maxima aud minima, in the fluctuations of the irregular 

 movement. Hence, we may conclude, that it is important, 

 in the first place, to employ three readings in preference to 

 any greater number ; and, secondly, that it is desirable that 

 the time of vibration of the magnet itself should be as small 

 as possible, consistently with the accuracy of its indications 

 in other respects. 



Professor Lloyd read the following extract of a letter 

 from the Rev, George S. Smith, containing some facts rela- 

 tive to the storm of May QGth and 27th. 



