94 REPORT—1846. 
this comprehensive task, found his leisure hours unequal to its completion. 
Now, on the contrary, the support of the British Association has enabled and 
induced this gentleman to suspend his other official duties for the year just 
expired, and to devote himself entirely to the prosecution of the work in 
question, in which his success will, I think, be appreciated by the Association, 
from the results which I have the pleasure of laying before you, accompanied 
by some remarks on the means employed to obtain them. What proportions 
these one year’s results bear to the final term of the whole labour, and how 
far they deserve to be continued, is a subject which I shall take the liberty 
of touching upon at the conclusion of this paper. 
The object of the calculations committed to my superintendence may be 
stated to consist in finding, by a sufficiently large series of observations, 
twenty-four corrections,— 
BY, AGP Ry ERO wets tyhshi ves nen cve va Ag'!, Ahi}, 
to be singly applied to the twenty-four preliminary values, 
g*, g*, hts, ht? AOC ew eee eee sereeeeesoes g, 1,1, 
which M. Gauss assigned to the constants of terrestrial magnetism, and in 
calculating at the same time the probable errors of the so-corrected constants. 
To this effect (preserving the literal denominations used in M. Gauss’s theory 
of terrestrial magnetism, and marking by AX, AY, AZ, Aw, wAd, pAi, the 
differences (theoretical value—actual (or observed) value)), the following 
expressions have been derived :— 
0=AX + Ag!°sinw—cosu(Ag')!.cosA + Ah!.sin A) +2 cosu.sinu.Ag®° 
—cos 2u.(Ag*®!.cos A+ Ah®!.sin A)—sin 2 w(Ag??.cos2A 
+ Ah®2. sin 2a)+3 -Ag°.( cos? u—=)sinu—( 3 cos? u—2 cost). 
(Ag3:!. cos A+ AA3:!. sin A)—sin %.(3 cos? w—1)(Ag>?. cos 2A 
+ Ah3*.sin 2A)—3 cos wu. sin? u(Ag>3 . cos 3 A+ Ah3.5 .sin 3 A) 
27 
3 , 3 (1.) 
+4(costu—5 cos w)sin u.Agt?— (4 cos u* 7 cos? % ++ =) 
(Ag*!.cos A+ Ah*! sin A) —2(2 cos’ —F00s usin u.(Ag**.cos20 
+ Ah**.sin2A)—(4:cos*u—1)sin?u(Ag*.cos 3 A+ Ah*3. sin 3A) 
—4 cos u.sin’ u(Ag*:+.cos 4A+ Att. sin 4A). 
O=AY + Ag!!.sinA—Ah!s! . cos A+ cos u (Ag®:! . sin A—Ah®! . cos A) 
+2 sinu(Ag®?.sin2 A—Ah**.cos2A) + (Ags:!.sin A — AAS! cosa). 
(cose u-=) +sin 2 u.(Ag’:?. sin 2 A—Ah3:2 . cos 2 A) 
+8 sin? w (Ag%-’ . sin 3 A—Ah33 . cos 3A) + (cos? u—= cos u). (2.) 
(Ag*!.sin A—Ah*!.cos A)+ (2 cos? u—; sin u(Ag+?.sin2 a 
—Ah*? cos 2A)+3 cos uw. sin? u (Ag*> .sin 3 A—Ah*3 cos.3 A) 
+4 sin’.u (Ag**. sin 4 /—Ah*+* .cos 4A). 
! 
y 
