xliv Introduction to the Makeestoun Observations, 1843. 
needle) were altogether omitted,* these 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 
y 1 be the sum (or mean) of the micrometer readings for the first day in the series, 
7/2 for the second day, . ... '. y D for the n th day ; 4, t 2 . . . 4 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 1 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 : — 
Vx - Vi - - a - (t L - t,) y p - y P+1 = - a - (t p ~ t p+1 ) c( 
y x - 2/9 = ~ 2 a-(* x - h) <f y p - y p+2 = - 2a-(t p - t p+2 ) c[ 
— 2/n+i = - » a - (ft— 4+i) <i y P - y P+ n+i = — » a — (t p — t p+nil ) g' 
Summing all those equations in which a has the same coefficient, naming the dif- 
ferences y p — y pi .i, A yi ; t p — a t h and since if t x ^> t 2 , then y x <^ y 2 , we shall have 
the equations 
2 A Vx _j a 
z — = / + 
2 A Ij A t 0 
2 A Wo , 2 a 
— q + 
2 A t> * A t 0 
2 Ay» , na 
2 A; t n Al 0 
* It will bo evident, that the method of obtaining the value of the unit for the balance niao-netome- 
tcr, described No. 51, supposes no other source of error than that due to the varying time of vibration, 
or that tho causes of error indicated above are of the second order compared with it. 
f Tho 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. 
■ 
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