Temperature Coefficient of the Bifilar Magnet. xlvii 



69. A series of days being selected in which the magnetic irregularities are 

 small, and in which the variations of temperature are as considerable as possible, if 

 we compare the mean instrumental readings for any two days, and if a R be the 

 difference in scale divisions, this difference is due to change of temperature of the 

 magnet, and to change of the horizontal component of the earth's magnetism, let the 

 portion of change of reading due to the former = A, and to the latter = a X, so that 



aE = A + aX. 



If the difference of the mean temperatures of the magnet for the same two days 

 be a t, then the correction for 1° of temperature in scale divisions 



At 



whence 



aE. _ aX_ 



At At 



Let a series of such values be obtained by comparing the mean scale reading, and 

 mean temperature of the magnet for each day with those for each day following in 

 the period selected : if we consider the differences a t positive, when the succeeding 

 day's mean temperature is less than that for the preceding day, and sum the whole 

 number of differences for which a t is positive,* then 



_ 2aR _ 2aX 

 lAt 2 At 



If we neglect the last member, the whole error of the determination of q" will 

 depend on the sum of variations of the mean horizontal force 2 a X ; as in a sufficient 

 number of determinations, it is probable that these variations will be as much posi- 

 tive as negative, and, therefore that the numerator will nearly vanish, the last mem- 

 ber may be neglected in the determination of q', and this with the more accuracy 

 the larger the sum of the differences of temperatures a t. Again, if the differences 

 for which a t is negative are summed, we shall have 



. 2 aR 2 aX 



' 2a? 2 a t 



The sign of the first member on the right remains as before, since a R also 

 changes sign. Reasoning as in the previous case, 2 a X may be supposed nearly 

 zero, and the last member of the equation negligible. If, however, the supposition 

 that the sign of a X varies positively and negatively with reference to the sign of 

 A t be inaccurate, it must be supposed either that the horizontal component remains 



* If tte scale readings increase with increasing horizontal force, A R will generally be negative 

 when A f is positive, and vice versa. The sign of a t is used as the argument, so that if A R be 

 positive when A i is positive, that value of A R will be subtracted from the sum of differences 2 A R. 



