380 DR. C. CHREE: ANALYSIS OF RESULTS FROM THE KEW MAGNETOGEAPHS 
Fig. 15. Year. 
The curve is really drawn from Cartesian co-ordinates, 81 parallel to MM', and 
cos I 8D (or here -385 SD) perpendicular to MM'. Increasing I answers to movement 
towards the foot of the paper, increasing D to movement towards the readers left 
hand. The hours are counted and marked as in hgs. 8, 9, 10 and 11, to wdrich the 
figures now under discussion bear a general resemblance. 
dhe angular distance of the needle from its mean position for the day is seen to 
be greatest about 1 p.M. , though m June the distance at 8 a.m. is nearly as great. 
The approach to the mean position is closest shortly after midnight, or else 
about 5.30 p.m. 
Ihe movement perpendicular to the magnetic meridian is considerably larger than 
that in che meridian. The curves for March and for the vear are oriented, so to 
speak, approximately magnetic east and west. The orientations of the June and 
Hecember curves are almost equally inclined to this direction, but on opposite sides. 
The curves of the second type were employed by the late xldmiral Capello in a 
paper in the ‘ B. A. Report for 1898, p. 750, dealing with diurnal inequalities at a 
variety of stations. They w^.re also used by Sir A. Rucker in a Rede Lecture to 
illustrate the actual motion of a freely suspended needle on a magnetic quiet dav, 
shov 111 ^ th e average non-cyclic effect experienced at Kew. In the present case the 
curves of both types answer to the strictly periodic part of the diurnal motion. 
Analysis of Diurnal Ineipiality in Fourier Series. 
§ 31. The diurnal inequality of an element may be expressed in either of the two 
equivalent forms 
a-^^ cos t I sin t + a. 2 cos '2t + [>2 sin 2^ + . . ., 
sin -k aj) 4- m sin {2t + ot,^) + . . . 
