XXVI 
Introduction to the Makeestoun Observations, 1843. 
it was laid down at the same distance, and with the north pole in the same direc- 
tion as before. In general, the vibrations were small, seldom above 10' ; when 
larger, it was checked by slightly approaching or removing the deflecting bar at 
proper times, with reference to the directions in which the suspended magnet was 
moving. Mr Welsh observed the bi filar magnetometer before and after each com- 
parison, and I observed the temperature of the deflecting bar after each comparison 
by means of a thermometer lying beside it.* 
28. After the deflection observations, the deflecting bar was vibrated in the 
declinometer box; it was suspended in a stirrup of silk of the same kind as that of 
the suspension thread, a small slip of paper was gummed to the extremity next the 
telescope, and the transits of the slip were observed. 
The following equation is then obtained : — 
mX=-~-^l+k (6-500) J 
• a 2 + b 2 
where K is the moment of inertia of the magnet = — — — M, a being 1 the length 
° 12 so 
of the magnet = 1*25 feet, b the breadth = 0-0719 feet, M the mass = 6216-7 grains. 
7T, the ratio of the circumference to the diameter = 3-1416, T, the true time of 
observation = T' ^1 + ^| - ; X' being the observed time of one vibration, 
H 
— as already defined (15.) and determined from the value 0*001465 for the declina- 
tion magnet thus j the moments of the declination magnet and deflecting bar are 
as jyjjjrj? the value of ^ for the deflecting bar is therefore = ° = °' 00155 62, 
a and a' are the semiarcs of vibration at the commencement and termination of 
the observations of vibration. The factor {1 + k (6-500)} is the reduction of the 
value of X to the bifilar reading 500, b being the mean bifiiar reading during vi- 
brations. 
The temperature of the bar during vibrations is observed, and the value of m is 
reduced to this temperature in the formula for deflections. 
29. Observations of deflection Averc made on August 12 and 21, November 8 
and 14, and on December 18. The observations on August 21 and November 8 
were reduced by the method of least squares, the equations of condition having the 
form 
+ £ + i |=o 
r- r l \ r s tan u X 
* It was soon found that good observations could only be obtained on cloudy days, as the sun heated 
the building on cloudless days to such an extent as to produce internal aerial currents. On account of the 
manipulations with the deflecting bar being performed outside, rainy days would not do, and it was found 
desirable that the days should be calm ; independently, then, of the necessity for a magnetic calm, there 
was requisite for a good observation a day cloudy, dry, and calm. 
