Lovering and Bond on Magnetic Observations at Cambridge. 15 
arc of vibration is to become shorter for every new excursion, and 
if the arc be of considerable length this circumstance must be taken 
into account. As the decrease of arc must be nearly uniform for a 
few vibrations, this is done by noting the limits of three successive 
excursions, and the mean of two means thus obtained is the true 
position of the bar for the middle time. Thus, if a, 6, c are the read- 
ings, x (+ (atb)+2 (b+c)) or + (a+2b+c) gives the place of the 
magnetic meridian for the time when 6 was observed. If the arc 
of vibration is very small, this correction will be inappreciable and 
the mean of two observations will suffice. But the declination itself 
meanwhile may vary by sudden and irregular movements, and then 
the process of observation and reduction becomes more intricate. 
Facts assure us that the magnetic meridian is subject to abrupt and 
lawless fluctuations as well as uniform and progressive variations. 
The practical mischief of these disturbed motions is diminished by 
the fact that they will most probably occur during periods of unusual 
perturbation ; and although they must be kept in view when study- 
ing the laws of remarkable derangements of magnetic influence, 
their effect will be insensible in the regular and periodic changes. 
A greater difficulty that affects particularly simultaneous obser- 
vations is this. The precise moment of time to which the mean 
result corresponds may not be that for which the declination is 
sought; and the interpolation of the required times between the 
observed times is a matter of troublesome and uncertain calcula- 
tion. ‘This labor is prevented by an ingenious device of Gauss, in 
the way of observing. If two observations of a bar are made at an 
interval equal to the time of one vibration, the mean is the place for 
the intermediate moment. This is a proposition mathematically 
exact, if the change of declination can be regarded as uniform and 
the arc of vibration constant. It will, therefore, be practically true 
