TEMPERATURE 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 ¢. 
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 :— 
TAYp — 2AYpie — 7 
SAN SV Al es At 
Summing these series of equations, we obtain the following :— 
5 (Fou — 52%) a g(pae — Eat) 4 _ _mti.n.n—-1 a 
ee yee AG BDA bab.) 6 RE 
Summing equations (1.), we have 
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 3 y, 32, 
each sum, from June 1 till June 26, was then compared with all the sums following, 
up to the 27th day after. The differences will be found in the following Table in 
two portions, namely those for which ¢, is greater and less than ¢,,,. The results 
for a second period, namely, from August 4 till September 18, 1844, are also given. 
Tas_E 15.—Results of Comparisons at different Intervals. 
by > btr t < to+r 
Interval 
between 
compari- No. of 2 sane 
ae compan —2A Y) =A (2) ai) Be ZA Yy) — ZA @) ae (y) 
sons. —ZA (¢) 
Mie. Div. S Mic. Div. Ss Mic. Diy. 
1149-8 102.8 D 2916-7 325-8 8-9 
2050-1 224.4 . 3925-7 | 477-0 
3171-6 | 379-2 ‘ 4341-2 | 541-4 
3879-0 | 446-5 : 4012-0 | 496-0 
3230-8 386-2 . 3552-0 421-4 
2967-8 316:5 E 3035-0 363-6 
2403-0 277-2 : 5294-4 685-2 
1857-9 210-0 : 5314-9 694-1 
1391-3 167-9 : 6094-5 775-1 
782-0 96-1 . 5281-9 724-6 
1853-8 196-0 : 5793-0 | 732-5 
1558-0 210-0 : 5488-3 669-2 
1439-6 192-0 . 5656-1 734-5 
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MAG. AND MET. oss. 1843. m 
