xliv Inteoduction to the Makeestoun Observations, 1843. 



needle) were altogether omitted,* tliese induced me to apply a correction obtained 

 by a method which first occurred to me in 1842, for the purpose of avoiding the 

 necessity of removing the needle and breaking up the series of observations. This 

 method has already been described, and the final results have been given in the 

 Transactions of the Royal Society of Edinburgh (Vol. xvi., p. 73) ; the coefficients 

 obtained by this method were used for correcting the results of the observations of 

 1841 and 1842 ;f they have also been used in correcting all the observations in 

 this volume. It will be necessary to enter more fully into the investigations here. 

 63. A series of days being selected during which the readings of the instru- 

 ment seem regular (rejecting any day of marked disturbance), and in which the 

 changes of temperature from day to day are considerable ; the hourly or two hourly 

 readings for the position and temperature of the needle are separately summed ; if 

 ?/i be the sum (or mean) of the micrometer readings for the first day in the series, 

 3/2 for the second day, . . . 2/„ for the 'd^ day ', ti, ti . . . tn being the cor- 

 responding sums (or means) of the thermometer readings, if q be the temperature 

 coefficient in micrometer divisions, and it be assumed that the vertical force changes 

 gradually throughout the period, a being the sum (or mean) of the daily changes 

 for all the hours summed for values of y^ y.2, &c., we shall then have a series of equa- 

 tions like the following, in which it is considered that the temperature of the pre- 

 ceding day is either greater than that of the succeeding in all the series, or that it 

 is less than it : — 



^1 - 3'3 = - 2 a~(ti - 4) g' Vp- Vp^i = - 2a-(tp- /p+2) gf 



(1-) 



^1 - y«+i = - na- (t^- t„+i) q' 1/p- y^+n+i = -na- (tp- /^+„+i) q' 

 Summing all those equations in which a has the same coefficient, naming the dif- 

 ferences yp — 3/p+i, ^ 3/1 ; tp — tp^i, A ti, and since if t^ ^ ti, then 3/1 ■<^ 3/2? '^^ shall have 



the equations 



2 At/. , a \ 



Z — =9^ + — 

 2 A /, A ^, 



"0 



2 A w, , 2 a 



— =?^ + 



2 A /2 A ^0 



(2.) 



2 A ?/„ , n a 

 2 A ^„ AIq 



* It will be evident, that the method of obtaining the value of the unit for the balance magnetome- 

 ter, described No. 51, supposes no other source of error than that due to the varying time of vibration, 

 or that the causes of error indicated above are of the second order compared with it. 



f The temperature coefficient, obtained by the usual method, had been applied, and the observa- 

 tions so corrected had been printed before I had satisfied myself of the preferability of the new coefficient. 



