48 Lovering and Bond on Magnetic Observations at Cambridge. 
Here we close our investigation of the diurnal magnetic curve. The 
existence of such a curve regularly formed every day cannot be 
doubted ; its general uniformity is also very observable. ‘The limits 
of the times of maximum and minimum declination in different longi- 
tudes show conclusively that it is in some way connected with local 
solar time. Developing the declination according to the most gener- 
al form of periodic functions we have obtained the preceding formule 
from which the empirical curves drawn on Plate V. were calculated. 
These calculated curves stand there side by side with the mean ob- 
served curves by which the constants of the formule were deter- 
mined. The calculated curve, as we might expect, is less broken 
than the mean curve; still, the two agree in a striking manner and the 
greatest deviations are in those months which suffered most from 
magnetic perturbations. In June and August the empirical curve and 
the mean curve keep close together and these were periods of unu- 
sual magnetic repose; for in the mean of the latter month the disturb- 
ed Term-day was omitted. June was most quiet of the two, and 
shows it by a superior agreement between its mean and empirical 
curve. If there were no permanent change of declination but only 
the daily oscillation uninterrupted by disorderly fluctuations, the me- 
ridian would swing day after day through the same arc; and a few 
observations would be sufficient to establish a rigorous formula 
which would evolve an empirical curve strictly coincident with the 
observed curve. The want of this uniformity is felt in the variation 
of the constants of the formule already given. This simplicity 
does not exist in the motions of the heavenly bodies any more than 
in the magnetic movements. But the analysis is different. In as- 
tronomy we know the cause of the disturbance and allow for it at 
once without deranging the general analytical expression. In the 
other case we have no theory, no hypothesis ; and the mathematical 
