208 ON DETERMINATIONS OF THE ABSOLUTE VALUE, SECULAR CHANGE, 
a the interval in months between the date of X' and March the 1st, 1847, and y the 
monthly variation occasioned by secular change. We have fifty-two such equations 
furnished by the series, which, treated by the method of least squares, give 
X=3'53043, and y= — *000347 the monthly secular change, the latter number being 
equivalent to an annual decrease of *0042 in the horizontal force during the period 
compi’ehended by the observations. For the purpose of obtaining the errors remain- 
ing over on this hypothesis of secular change, we must apply to each of the results in 
Table I. a correction, equivalent to the elfect of secular change in the interval elapsed 
between the dates of the particular observation and the mean epoch of the 1st of 
March, 1847 ; and having done so, we now find, on the hypothesis of the existence of 
a uniform secular decrease of the horizontal force annually of *0042, 3*53043 as the 
value of the horizontal force on the 1st of March, 1847, with a probable error of 
+*00025 ; whilst the probable error of a single monthly determination is reduced to 
+’0018 instead of +*0040 as before; and as the weights of different hypotheses are 
measured by the inverse squares of the probable errors, the hypothesis which supposes 
a secular decrease of force amounting to *0042 annually is more probable than the 
hypothesis which supposes no secular change, in the proportion of 4*7 (nearly) to 1. 
Having thus obtained the value of the horizontal component of the magnetic force 
corresponding to the 1st of March, 1847, and the mean value of the secular change of 
this element during the period of the observations, we require, for the purpose of de- 
riving the values of the total magnetic force and its seeular change, at the same epoch, 
to know the magnetic inclination corresponding to the epoch, and the secular change 
of that element also. For the first we have to seek the mean result of the observations 
of inclination, which were also made monthly during the same fifty-two months. In 
the three first years, 1845 to 1847 inclusive, the observations of inclination were made 
on every Tuesday and Friday, three hours before noon on the Tuesdays, and three 
hours after noon on the Fridays ; thus furnishing eight or nine partial determinations 
in each month according to the number of Tuesdays and Fridays contained in it; 
each determination being complete in respect to the several positions of the circle and 
needle required for that purpose. In 1848 and 1849 the same number, or occasion- 
ally a greater number, of partial determinations was made monthly ; but instead of 
the Tuesdays and Fridays, the days of observation were the same as those on which 
the horizontal force was observed. The circle employed, from January 1845 to 
March 1846 inclusive, was one of Gambey’s well-known 9-inch circles, and from 
April 1846 to April 1849 one of Robinson’s, of the same dimension and of the same 
pattern. In Gambey’s circle two needles were used, one from January 1845 to De- 
cember of the same year, and the second from January 1846 to March of the same 
year; in Robinson’s circle also two needles were used, one from April 1846 to August 
1847, when an accident befell it, and a second from September 1847 to April 1849. 
The needles used in Gambey’s and Robinson’s circles were made by those artists re- 
spectively, and both circles and needles were probably as perfect of their kind as any 
