26 C. A. Schott—Magnetic Declination in the United States, 
which are to be treated in the usual manner. To determine the 
value of a a, three (or more, if necessary) assumptions are 
made, and those stir whieh render =A? a minimum are 
reference to desirable epochs, special weights were assigned ; 
generally the observations received the weight unity, a few 
imperfect observations the weight one-half. Of observations 
evidently grossly in error, no notice was taken. 
second periodic term depending on r, a, ¢, could only 
be established for a few places, owing to insufficiency in the 
number of sees and their want of the greater accuracy 
demanded for i 
The annual ange v in the magnetic declination, positive 
when increasing west (or ae east), also the epoch 0 
minimum west declination (or of maximum east declination), 
also its amount and the apparent probable error of an observa- 
tion, are found as follows 
Differentiating the expression for D, we have 
dD=ra cos (am+e)dm+r,a, cos (a,m+ce,)dm+... 
hence for any time ¢, and for minutes of are, 
v= 60 sin 1°[ra@ cos (am+c)+r,a, cos (aym+c,)+...] 
Maxima and minima are deduced from the equation 
0=ra cos (am+c)+r,a, cos (a,m+e,)+... 
from which expression we can find m. 
The apparent probable error e of an observation is deduced 
from the differences 4 of the n observed and computed values 
by the formula 
BE hbo tod "45524" 
n—n, 
where n, equals the number of unknown quantities in the ex- 
pression of D, which had to be found from the observations; 
when weights, w , are used, substitute wa? for a2. ‘The greater 
part of this apparent probable error is due to the fact that the 
observations collected at any one station were not generally 
made at the same spot; it represents, consequently, local irreg- 
ularities in _ distribution of magnetisim, as well as pure 
observing error: 
The cemented uncertainty in the investigation arises partly 
from the large observing errors in the older observations, made 
with ordinary compasses or with rude aaa generally, 
and partly, since ape introduction of the refined instruments, 
