AND ITS TEMPERATURE CORRECTION. 75 
Placing the equations in the form 

ER ee ra 
age ike emer! git. so depen) 
Naming the differences in which r=1, ay, and at, in which r= 2, ay, and 
Aft, .... Ayn, At, Summing separately all the equations for a,, all those for 
iS It will simplify the investigation, and be sufficiently accurate to 
take for the divisor of ra, the mean of all the values of a ¢, naming this a h. 
We obtain the following equations: 

== a 
EpATG to 
ZA Yo _ a 
Se: Ad (9.) 
ZAYn _ n a 
3 A.te oe A hy 
If the difference of each equation be taken with every one following it, ano- 
ther series of equations of the following form will be produced. 
LAY, 2ZAYpsr ra 
She TA yas Smaaeaiihd ost 
Summing the equations thus formed, we obtain an equation which may be 
put as follows: 





ZAM TAY, ZA Yo ZA Yn-1 n+1.n.n—1 a 
aril —_ 4 2), at A eA de big = ry, Be : Z 
i a ae) 3(348 Tea 6 A ty ae 
Summing equations (9.) 
deme A ( n+1 a 
es AE sO D8 
16. The following example, from the Makerstoun observations, will shew the 
method found most convenient in practice for the summations. 
A period of 52 days, from June 1 till July 22. 1843, having been selected 
as nearly free from disturbances, and containing considerable changes of tem- 
perature, the 3d and 7th June being rejected on account of disturbances; the 
sums for each day of the micrometer and thermometer readings were entered 
into columns titled sy and s¢. Each sum was then compared with all the 
sums up to the 27th day after, and the differences entered into columns titled 

AY, At, AY Ah; . ~~ AY, Aty. Those differences, the fewest in number, 
in which ¢,= t,,, were marked out, the others summed for each column, and 
ss aA DAY: 
the divisions —“ |. . AAS Hoy 
Paee Se performed. 
From these and equations (11), (12), 

2A (y) te te ee Baty 
2 a (t) = 8:88; . 7 = 0.0875; @ = 2.05; g = 7.882 Mie. div. 
