844 DT;. C. CHREE: ANALYSIS OF RESULTS FROM THE KFAV MAC4NETOGRAPHS 
111 tlie present instance we get for the period 1891 to 1900, at Kew, 
8N = + 302y, SW = - 181y, 8V = - 208y. 
Thence we find SPt = TOOy, and its line of action makes with three rectangnlar 
axes drawn respectively to the north, tlie and vertically ‘upwards the angles 
42°-0, G3°-5, and 00°-0. 
'the projection of the line of action of 811 on the horizontal plane is inclined to tlie 
geographical meridian at tlie angle 30^’9, running in a nortli-cr/.s"^cr/p direction. 
Amival Ineqiiah'fi/. 
§ 10. If the secrdar change proceeded at a uniform rate throughout the year, the 
mean value E,, of anv element answerino: to the middle of the rf'* month of the vear 
should be derivable from tlie mean value E for the wliole year by the formula 
E, =E + (2a- 13).sV24, 
where .s is the secular change for tlie entire year. 
This neo'lects tlie differences between the lengtlis of months, as being for the 
IT) Os' 
present pur])ose immatei'ial. 
(fonver.sely, if one applies to E„ — E the correction — {2n ~ 13) .9/24, one eliminates 
the effect of a regularlv pi'ogresslve secular change, and obtains what is known as tlie 
“ Annual Inequalitv.” 
In jiractlce, complications arise from the apparent variability in the .secular change 
from year to year. To illirstrate the consequences of such irregularity, take the 
simple hypothetical case where the secular change of declination proceeds uniformly 
from January 1 to December 31 of a year at the rate of 12' a year, and then proceeds 
for the next twelve months at the nniform rate of O' a year. From the mean values 
for the two years we should deduce a secular change, not of 12' or of O', hnt of 9' a 
year, and if we corrected tlie two years’ monthlv values independently, on the 
assumption of a secular change of 9' a year, we should deduce for each year a wholly 
fictitious annual inequalitv. C’omhining the monthly values for the two years we 
should in this ease conclude, rightly enough, that there was no true annual ineipiallty, 
but that is merely an accident of the particular hypothesis. The illu.stration will 
show how uncertain is the physical interpretation to he put on an a})parent annual 
inequalitv in the case of an element wlio.se secular change is irregular, unless we deal 
wltli mean monthlv values from a large nundier of years. 
The results in Table IV. have been obtained 1)V combining 10 vears’ results for I, 
V, and T, and 11 yeans’ re.sults for the other element,s. The data assigned to the 
“ middle of the montli” are the values actually olitalned for the differences between 
the mean monthlv values and the mean annual \'alue after the ajijilicatlon of the 
