XIV INTRODUCTION TO THE MAKERSTOUN OBSERVATIONS, 1847 To 1855. 
similar to that described in the Introduction, 1845-46, pp. xl.andxli. The follow- 
ing are the results :— 
Value of & from the 






Deflection of Deflection of t 
Distance of Bar | Balance Magnet | Balance Magnet | formula k = FER, 
in Feet. in adjustment in | suspended hori- n tan dip. 
mic. divisions. zontally. (See Introduction, 
1845-46, p. xli.) 
(n) (u) 
2°5 PATE 47 37 0:0000226 
30 116-7 2616" 0-0000228 

As the value of &, thus obtained, does not differ much from that obtained by 
Mr Broun in 1848, the original value has been adopted in the reductions. 
The tabular corrected readings of the balance needle, before its change of 
plane, are found thus :— 
Let n denote the observed reading (generally negative), 
t the temperature Fahr., 
R the reading corrected by means of the temperature tables ; 
then 
R=1244+7-90 (t-26) +m. .  . (Introduction, 1845-46, p. xliii.) 
The quantity R being multiplied by the factor 0-00001, gives the variation in parts 
of force. 
After the change of plane of the balance magnet, the above formula became 
R=96'7 + 3°72 (t— 26°) +n, 
at least as far as may be inferred from the temperature tables then prepared and 
employed. 
It would seem, however, that some change in the zero of the instrument took 
place at the time of its change of plane, which was not embodied in the tempera- 
ture tables. This change appears, however, to have been recognised in the General 
Results, p. xlv., in a table which contains the monthly means of the vertical com- 
ponent of the magnetic force from 1842 to 1849, and consequently this table furnishes 
the means of estimating the change. It would seem that R, or the quantities 
found in the daily observations under the heading “ Balance corrected,” require, 
after the date of change, to be diminished by the quantity 118:0, before being 
multiplied by their appropriate factor 0-0000212, in order to give forces com- 
parable with those obtained before the change. Hence, before the change— 
f=R x 00000100) “S ~ *  . (Resuilts’ 1844p. S75.) 
After the change, 
f=(R —118-0) x 0-0000212. 
It was thought that by this means the observations, after the change of plane, 
might be made comparable with those before ; nevertheless, Mr WELSH advised that 
they should be treated as two distinct series. 

