46 Lovering and Bond on Magnetic Observations at Cambridge. 
Plates IV. and VI. will show how rapidly the series of both formu- 
le converge and the limit of error incurred by dropping all the 
terms after the 5th. In the formule. for October the 5th term of 
the declination cannot exceed ,034 of a minute and the 5th term in 
the value of the temperature cannot be greater than ,4 of a degree 
of Fahrenheit. From the nature of an empirical curve our confi- 
dence in it must bear some proportion to the accuracy of the obser- 
vations. If these observations are exposed to errors from any cause, 
as we have seen that they are, the empirical curve will suffer, 
though in a less degree, on their account. The error which ina 
single diurnal curve is left in its naked state is of course diminished 
in the mean curve of several days by the levelling influence which 
all the days exercise upon any single one. But this process reduces, 
it does not extinguish the error. The passage from the mean of 
the observed curves to the empirical curve carries us one step fur- 
ther towards the true expression of the actual phenomena of mag- 
netism. Fora considerable mean error arising from irregular dis- 
turbances, which in the first is concentrated upon a single moment, 
will be in the second curve distributed over the whole day and may 
therefore disfigure the general character of the day though it does 
not distort extremely any particular part. Moreover, it is easy in 
calculating the values of the constants in the empirical formula to 
omit observations of an extraordinary character and which are no- 
toriously burdened with strange anomalies. This we see on Plate 
V. in the instance of the September days and to a less extent in 
October. The whole character of the curve for the former is 
changed from what we have reason to believe is the real diurnal 
curve ; although it has escaped those large and prominent excur- 
sions which appear three or four times in the mean of the observed 
curves. In seasons of great disturbance it would be more safe to 
rely on the empirical curve than the observed curve ; but in quiet 
