On the Magnetic Declination at the Magnetic Equator. 385 
follows, 
H’, +h’, A HW’ +A) +0’, ... HY", +h", 42", 
H+", 42" en Pr eee 
n—1 n—-l A-1 : n n n 34 n n 
Ht” +h, +v,, Ho +h +a,... Hi +h),+z,,- 
Bhisisintng these quantities we have, 
eh) 0 (td) ,0 i O (24) 
2) f+ 2h, + Ew ? H+ 2h +4, 1% H+ dh +%,,% (C) 
and for the A 
O+Ah, $= 
In this case © is the mean di it observations, of which 24 give 
the true means for the total solar influence, and the remaining n—25 
being equally distributed through the hour-angles also give the mean 
approximately. 
Instead, however, of combining the observations in this way, the 
following method has been preferr ed. Let, in the quantities (B), 
(H,) = 1,4 ¢ += 
a ae opis ee ape. 
Gs Untig 
Then H’,+ 2’, e a’, — aj h', +. (@',. ye; 
a + i" ot a” i- CH, fen Es + wn = d", 
ol ae ig nu— nt )= a (ae 1) = ee 
Summing the fi two shinies we have 
awe 
2d, ab fag 2 (#’) 
nm—\1 } n—1 
Similarly we obtain 
xd, 2. a 
af eis and so on. 
n—1| 
Loh + 
It will be observed that in these summations there are two assump- 
tions ; one, that the lunar diurnal law is constant throughout the 
lunation, or series of lunations, for which the means are obtained ; or 
that the quantity € in the expressions (B) is constant. If this be 
not exact, thea the quantity — will contain the variation due to this 
n 
cause, and depend in part on the lunar hour-angle ; so that the mean 
(H.) which is employ ed in taking the differences will eliminate part 
of the lunar action and partially distort the law. The other assump- 
tion is that the mean solar diurnal variation, represented by (H,),(H,) 
»..., 18 nearly constant throughout the period ; for, if not, the dit- 
Phil. Mag. S. 4. Vol. 21. No. 141. May 186}. 2C 
