AND ITS TEMPERATURE CORRECTION. 75 



Placing the equations in the form 



'-^^^' = T^+9 (8.) 



Naming the differences ia which r = 1, a?/,, and a A, in which r = 2, a^j. and 



A^2 . . . . Ai/„, At„. Summing separately all the equations for ai, all those for 



Aj It will simplify the investigation, and he sufficiently accurate to 



take for the divisor of r a, the mean of aU the values of a t, naming this a U 



We obtain the following equations : 



2 A wi a \ 



- q + — 



2 A 4 A /o 



2Aj^_ 2a^ 



2 A /2 ^ A 4 



2A,y„ _ na 



lAtn ^ A to 



(9.) 



If the difference of each equation be taken with every one following it, ano- 

 ther series of equations of the foUoAving form will be produced. 



2A^y 2A,Vptr _ ra^ qq -v 



2 A/, lAtp„ Ato ' ' ' ^ '' 



Summing the equations thus formed, we obtain an equation which may be 

 put as foUows : 



Summing equations (9.) 



1 ^ 2A(i/) n + 1 a_ j2) 



^ M ^ 2 A (/) 2 A /„ ^ ' 



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 tiU July 22. 1843,^ having been selected 

 as nearly free from distm-bances, 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 2y and 2t Each sum was then compared with all the 

 sums up to the 27th day after, and the differences entered into columns titled 

 Ai/i, At,; Ayi, aU.; . . . . A^og, a ^26. Those differences, the fewest in number, 

 in which t^, :^ t^,^^ were marked out, the others summed for each column, and 



the divisions |^ .... |^ performed. 



i A fi 2 A ;26 



From these and equations (11), (12), 



2 1^ = 8.338 ; ~ = 0.0375 ; a = 2.05 ; g = 7.832 Mic. div. 



2i A (j; A to 



