DISCUSSION OP THE VERTICAL FORCE. 7 



The last column contains the mean readings. They may be represented by the 

 equation : — 



where a;= montlily amount of loss of magnetism and effect of secular change. 



?/= change in magnetometer reading for a change of temperature of 1° F, 

 Ae= epoch — middle epoch. The middle epoch is January 1st. 

 At= temperature — mean temperature. 

 y„= mean reading of the vertical force magnetometer. 

 V= any of the monthly means to be represented. 

 From the 12 conditional equations, we form the normal equations 

 — 828.90= + 143.000 x— 85.335 y 

 + 4685.73=— 85.335 07 + 443.120?/ 

 whence a; ^ + 0.577, the monthly change, equal to nearly 7 scale divisions for 

 each year. 



And ?/= + 10.68 scale divisions, the correction for temperature for 1° F. This 

 is not quite three-fourths of the value found by direct measure. 



Second determination of the temperature coefficient by means of alternate com- 

 binations by seasons. 



The mean values for each season have been directly formed from table No. 1. 

 The value in June, 1845, is necessarily omitted. 









Alternate means. 



Differences. 



Temp, 

 coefficient. 



1841 



1841-2 



1842 



1842-3 



1843 



1843-4 



1844 



1844-5 



June toNovemljer 

 December to May 

 June to November 

 December to May 

 June to November 

 December to May 

 June to November 

 December to May 



6333.3 

 657.2 

 758.4 

 670.4 

 779.5 

 719.6 

 846.5 

 690.6 



660.89 

 66.03 

 72.88 

 63.27 

 73.28 

 63.53 

 72.17 

 61.55 



695^.8 

 663.8 

 769.0 

 695.0 

 813.0 

 705.1 



690.88 

 64.65 

 73.08 

 63.40 

 72.72 

 62.54 



+38^.6 

 —94.6 

 +98. 6 

 —84.5 

 +93.4 

 —141.4 



+30.85 

 —8-. 23 

 +9.81 

 —9.88 

 +9.19 

 —9.63 



IC.O 

 11.5 

 10.1 

 8.6 

 10.2 

 14.7 



Mean 



10.85 



By preceding method 



10.68 













Mean, adopted . 





10.77 



We have for the reflecting magnetometer Ic := 0.000033 



-^-= 10.77, hence q=^: 



0.000355. For comparison we have the corresponding values at Toronto -^-^ 1.80 



and ^=0.000113. 



The scale value Jc at Toronto is 0.0000628, nearly twice as large as at Philadel- 

 phia. The comparatively large value for q at Philadelphia is most probably due to 

 the large size of the bar which prevents a thorough hardening, a circumstance 

 which undoubtedly also contributes to the difference exhibited by the resulting 

 value of q as found by the direct and indirect methods. 



The magnitude of the temperature coefficient requires that the standard tempera- 

 ture should be the mean temperature at all the readings. The average temperature 

 between February, 1841, and June, 1845, is 66°. 0, which has been adapted as the 



2 



