270 
LITTLEHALES. 
of the period of observation. With the increasing impor¬ 
tance of a knowledge of the magnetic dip or inclination in the 
navigation of modern vessels of commerce and of war, atten¬ 
tion was turned to the deduction from the collected observa¬ 
tions of empirical equations representing that element at the 
various stations with a view of predicting values at these 
places and of arriving at appropriate methods for bringing 
forward to the present or some future time the isoclinic lines 
represented on the magnetic charts for past epochs. 
The empirical equations thus deduced are stated in con¬ 
nection with the observations from which they have been 
formed. In a few cases the conditional equations were ex¬ 
pressed as a series of powers of the form V=A-\-Bt+Cf; 
but, in all cases in which the extent of the series of observed 
values w r as sufficient, a harmonic function with an assumed 
period of the cycle was employed in the following form: * 
V = A 4- B sin t 4- C cos t in which V represents 
m m 
the declination or the inclination, m the period of the cycle, 
t the time in years and fractions of a year reckoned from 
some assumed epoch, and A, B, and C constants that are 
determined from the observations by the method of least 
squares. 
It may be useful to make it known that my later work in 
the deduction of these equations was facilitated by finding 
the correction to the assumed period, which was necessary to 
bring about a reasonable accord between the observed values 
and those computed from the deduced equations for the cor¬ 
responding times, instead of assuming several values of the 
period and, after performing all the work of deduction for 
each, selecting that which gave the most accordant set of 
computed values or the smallest probable error of a single 
observation. 
The most vital objection to the method first followed is 
that there is no ready means of ascertaining when the best 
empirical equation that the observations will yield has been 
obtained. 
