Tempeeature Coefficient of the Bifilar Magnet. xlv 



whence 



' - ^ _ ^^ 



^ ~ Ai 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 ^ is positive,* then 



. 2aR 2aX 



2 A ^ 1. 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 temperature 2 a t. Again, if the differences 

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



2 A R 2 aX 



g'= + . 



^ 2 A ^ 2a; 



The sign of the first member on the right remains as before, since a E, 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 i be inaccurate, it must be supposed either that the horizontal component remains 

 constant, and therefore, that a X = 0, or that it varies in one direction only, in- 

 creasing continuously, or diminishing continuously, throughout the period selected, 

 and, therefore, that the sign of a X is the same for both equations. In the latter 

 case, it is evident that by taking the mean of the values of q' from the two equations, 

 the last members will nearly destroy each other. It has been supposed that the 

 variations of X are altogether independent of the variations of the temperature, a 

 supposition which is borne out by every method of examination of the results. The 

 details of a series of comparisons are given, pages li., lii., and liii., Introduction, 1843, 

 from these it appears : 



70. Isi, That the value of q' is the same, when a sufficient number of compari- 



* If the scale readings increase with increasing horizontal force, A E, will generally be negative 

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

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



MAG. AND MET. OBS., 1845 AND 1846. m 



