68 Lovering and Bond on Magnetic Observations at Cambridge. 
log. bi + log. cos. ( 2+ Bi) = 1.55579 = -++ 35.96 = bi cos. (2+ B' ) 
log. bii + log. cos. (22 + Bi) = .95669=-+4+ 9.05 = b" cos. (22 + Bi) 
log. bii 4- log. cos. (34 + Bill) = 1.09840 = — 12.54 = bill cos. (32 + Bi) 
log. biv + log. cos. (44 + Bit) = .71294 = + 5.16 = db" cos. (44 + B*) 
Y= 437.6 
-+ 300.00 = c° 
log. ci + log. cos. ( 4+ Ci ) = 2.34214 = + 219.85 = ci cos.( 44 C') 
log. cii + log. cos. (22 + Ci) = 2.18394 = + 152.74 = cli cos, (24 + Ci) 
log. cii + log. cos. (32 + C') = 1.61370 = — 41.09 = cili cos. (34 4+ Ci) 
log. civ + log. cos. (44 -+ Civ) = .78661=-+ 6.12 = cv cos. (42 + Cr) 
Z= 1637.6 
X, Y and Z being thus determined, if we represent the declination 
by 4, the inclination by 2, the total intensity by y and the horizontal 
intensity by w, we have these two formule to find 6 and w: 
X=weos. 6, Y=w sin. 0. 
Again ; 
w=ywycos.i, Z = y sin. 2. 
from which i and wy are deduced. 
log. Y = 1.57519 
log. X — 2.62961 log. X — 2.62961 
ef — tang, 5 = 8.94558 sec. 8 = 0.00170 
6 =5°4, 2.63131 — X sec. § = w= 427.9 
; 4 Z 
log. cosec. 1 = 0.01433 tang. 7 — 0.58290 — — 
w 
y = 1692.5 — 3.22854 — Z cosec. i 4 == 75° 22’ 
After dividing the numbers which represent the Horizontal and 
Total Intensity by 1000 to reduce them to the arbitrary unit in com- 
mon use, we have the following values of the elements for 1837, 
calculated according to Gauss’ formule. 
Computed. Observed. Difference. 
The Declination = 5 4’ OPM Oia Any) 5! 
The Dip = 75 22 | 74 22 | 1 00 
The Horizontal Intensity — 0.4279 
The Total Intensity = 1.6925 
