74 MR BROUN ON THE BALANCE MAGNETOMETER, 



would probably not be altogether in the vertical, the portion resolvable to the ho- 

 rizontal would affect the position of the needle. 



14. From these considerations I was induced, about two years ago, to endea- 

 vour to obtain the temperature correction from the usual daily observations of 

 the instrument. To most persons acquainted with the irregularities in the mag- 

 netical variations, from the changes of the magnetic intensity or its direction, this 

 might appear to some extent chimerical, and as at best only capable of giving a 

 rough approximation to, or verification of, the determinations by deflection. It 

 will, hoAvever, I think, be shewn, that a better coincidence of partial results, and 

 a better correction, may be obtained from this than from the usual method. 



It will not be necessary to point out the methods which were at first tried ; 

 I shall proceed at once to those which have been ultimately adopted. 



15. Having selected a series of days during which the readings of the instru- 

 ment seem regular, and in which the changes of temperature from day to day 

 are considerable, rejecting any day of marked disturbance, the hourly or two- 

 hourly readings for the position of the needle and for its temperature are summed 

 for each day. Let us designate the sum of the micrometer readings for the first 

 day of the series y, for the second day y., and so on to y-,-irv\'i the corresponding 

 sums of the thermometer readings being t^, t,, .... t.,,y^i, the number of the days, 

 from the beginning to the end of the period, being 2w + l. 



The most simple and probable hypothesis that can be formed, is, that the 

 mean vertical force increases or diminishes gradually throughout the period ; let 

 the mean daily change be a. 



If q be the temperature correction for 1° Fahr. in micrometer divisions, we 

 may form the following series of equations : 



2/i=2/- + a + (h -h)q !/-2=l/s + a + {t^ - h)q 



5^1 = ^3 + 2 a + (A - (-3 ) 7 y^- yi +2a + (J.- h)q 



yi = j/»+i + « « + (/i - if„+i) q y2 = yn^-i + na + {i^ - /„+i) q 



y„+2 = .'ATTs + a + (C+2 - t^i) q 



(7.) 



There will be breaks in each series, as there are no sums for the Sundays. As 

 ts may be greater than ti and t, the result of the comparison of yi Avith y, is not 

 equivalent to the comparison of ^i with y, and y, Avith y^. 



From these equations the most probable values of a and q might be obtained 

 by the usual methods ; but the labour which they demand is probably much be- 

 yond the greater accuracy to be attained. The following, it is conceived, wiU be 

 found sufficient. 



First classing the equations in which t^::^or^/,+„ and considering each 

 class separately. 



