Temperatuee Coefficient of the Balance Magnet. 



xlv 



where, as it tends to simplify the investigation, and is at the same time sufficiently 

 accurate, a t^ is the mean of all the values of a t. 



Taking the difference of each of the equations with that of every one after it, 

 series of equations of the following form will be obtained : — 



2 A ;„ 



2 ^^p + r 



2 At, 



p+r 



r a 



A L 



Summing these series of equations, we obtain the following : — 



\2 A ^^ 2 A 4/ ^ V2 A ^2 2 A ^„_i/ 



2 A 4 , 



Summing equations (1.), we have 



+ 



n + \ 



n . n- 



^L 



,. = i.2^AW 



n + 1 



a 



A^n 



2 A (0 2 



From these two equations q' will be obtained. 



63. A period of 52 days, from June 1 till July 22, 1843, was selected as nearly 

 free from disturbances (the 3d and 7th of June only being rejected on this account), 

 and as containing considerable daily changes of temperature ; the sums of the micro- 

 meter and thermometer readings for each day were entered in columns titled 2^, 2 ^, 

 each sum, from June 1 till June 26, was then compared with all the sums folloMang, 

 up to the 27th day after. The dijfferences will be found in the following Table in 

 two portions, namely those for which tp is greater and less than t^^^. The results 

 for a second period, namely, from August 4 till September 18, 1844, are also given. 



Table 15. — Results of Comparisons at different Intervals. 









fpy 



^p + r 







^.< 



^p + r 







r^ 



Interval 

 between 



















Mean 





















of the 



1 



compari- 

 sons. 



No. of 

 compari- 

 sons. 



-2A(y) 



2A(0 



-2A(^) 



No. of 

 compari- 

 sons. 



2A(y) 



-2A(0 



2A(^) 



results. 



2 A (t) 



- 2 A (?) 





Days. 





Mic. Div. 



o 



Mic. Div. 





Mic. Div. 



o 



Mic. Div. 



Mic. Div. 





1 



7 



1149-8 



102-8 



11-2 



11 



2916-7 



325-8 



8-9 



9-5 



. 



2 



7 



2050-1 



224-4 



9-1 



11 



3925-7 



477-0 



8-2 



8-5 



CO 



3 



9 



3171-6 



379-2 



8-4 



9 



4341-2 



541-4 



8-0 



8-2 



CO 

 1— 1 



4 



11 



3879-0 



446-5 



8-7 



8 



4012-0 



496-0 



8-1 



8-4 



(N 



5 



9 



3230-8 



386-2 



8-4 



10 



3552-0 



421-4 



8-4 



8-4 



(N 



6 



7 



2967-8 



316-5 



9-4 



11 



3035-0 



363-6 



8-3 



8-8 



i;^ 



7 



5 



2403-0 



277-2 



8-7 



17 



5294-4 



685-2 



7-7 



8-0 



1-5 



8 



4 



1857-9 



210-0 



8-8 



14 



5314-9 



694-1 



7-7 



7-9 



1 



9 



6 



1391-3 



167-9 



8-3 



12 



6094-5 



775-1 



7-9 



7-9 



ID 



10 



6 



782-0 



96-1 



8-1 



11 



5281-9 



724-6 



7-3 



7-4 





11 



7 



1853-8 



196-0 



9-5 



11 



5793-0 



732-5 



7-9 



8-2 



1-5 



12 



5 



1558-0 



210-0 



7-4 



14 



5488-3 



669-2 



8-2 



8-0 





13 



6 



1439-6 



192-0 



7-5 



13 



5656-1 



734-5 



7-7 



7-7 



MAG. AND MET. OBS. 1843. 



m 



