Lovering and Bond on Magnetic Observations at Cambridge. 47 
times, as the empirical curve borrows all its truth and expres- 
sion from these observations, the latter have more claim to 
consideration than the calculated places. It is obvious from the 
principle on which the empirical curve rests and the manner in 
which the constants are deduced that they will answer only for one 
curve and must be calculated separately for every new curve that 
is required. As the form of these equations and the time, which is 
the only variable, are the same for each curve, whatever changes 
exist in the diurnal curve from one month to another in the year 
must be indicated by a corresponding change in the independent 
constants. And moreover if there be, as the comparison of recent 
and old observations lead us to believe, secular periods for the mag- 
netic declination, they will betray themselves by slow variations in 
the mean yearly values of these same constants. It becomes then 
an object of curious inquiry to ascertain what are the values of .4, 
Ci, C2, Cs 3 ¢1, 2, €3, &c. for every month in the year; and after 
this their mean values from one year to another. It is possible that 
the laws of the secular changes may be better studied from the 
variations of these constants than from immediate observations. 
Four of these formule are here given with the names of the months 
to which they belong, and the number of days employed in calcu- 
lating them ; t = the time from 0" Gott. M. T. 
June, 10 days. Declination* 
= 9°17',8—3',853 sin (¢—1621m24*)—1! 537 sin2(¢—931m24»)—0/,948 sin3(#--027,,9.) —0/644 sind ((—4h22m9s). 
August, 4 days. Declination 
= 9°13!,9—3/,907 sin ¢—15"1247*)—2/009 sin 2 (t—946"58*)—0/,878 sin 3 (¢-+-0%51,,15s). 
September, 5 days. Declination 
= 921! ,9—2/,932 sin(t—9'3418s) —1/,530 sin2(¢—8"128*)—0/,494 sin3(¢-4-132m29s)—1/,090 sin4(t—029,,58:). 
October, 5 Days. Declination 
= 9°18!,7—1!,575 sin(¢—13'042*)—2/ 379 sin2(¢—10"40™58*)0!,508 sin3(t—04n58s)—0/,034 sin4(t+-0"12,,32,). 
* The first term in the value of the declination is obtained directly in parts of 
the scale and is afterwards reduced to absolute numbers in the usual way of 
deriving the real declination from the reading of the scale. This process will 
be soon explained. 
