ON THE MAGNETIC DECLINATION. 



9 



The two values for 1843, marked (a) and (&), exhibit the separate sums for the 

 bi-hourly and the hourly observations, and were required to give proper weights 

 to each. There are 37 months of bi-hourly, and 21 months of hourly observations 

 the latter having double weight, as found from a consideration of the probable 

 errors derived respectively from all the results of the years 1842 and 1844. The 

 probable error of any single monthly mean for any hour in the year 1842 was 

 found = + O d .60, and the same for the year 1844 was = + O dl .40. Hence the 

 weights for a resulting value in the bi-hourly series is to the weight for a value in 

 the hourly series nearly as 1:2, or the weights are nearly proportional to the 

 number of observations a result which indicates that no constant errors influence 

 the result. The accordance among themselves of the values for the easterly hour- 

 angles is somewhat better than the corresponding values for the westerly hour- 

 angles a circumstance which seems to connect itself with another phenomenon to 

 be mentioned presently. Giving, therefore, double weight to months of the hourly 

 series, the lunar-diurnal variation resulted as given above. When expressed 

 analytically, it takes the form 



A c = +0'.001 + 0'.029 sin (0 + 295) + 0'.207 sin (29 + 85) 

 which may also be written 



A C = 0".0 + 1".7 sin (15n + 295) + 12".4 sin (30rc + 85) 



where represents the moon's hour-angle, reckoned from the upper culmination, 

 or n the number of hours after the same epoch : -f indicates west, and east 

 deflection. 



