Similarly we may take the up and down swing, find the average amount of it throughout the year, and again we shall find that this corresponds very closely with the average number of sun-spots. [Illustration: PLATE XII. NUMBER OF SUNSPOTS (Wolf) Compared with DAILY RANGE of MAGNETIC DECLINATION & DAILY RANGE of MAGNETIC HORZL. FORCE (as observed at Greenwich.)] [Sidenote: Daily curves.] [Sidenote: Difference between summer and winter, and between sun-spot maximum and minimum.] [Sidenote: Cause unknown.] But perhaps the most striking way to exhibit the sympathy is to combine different variations of the needle into one picture. And first we must remark that there is another important variation of the earth's magnetic action which we have not yet considered. We have mentioned the swing of the needle to and fro, and the swing up and down, and these correspond to changes in the _direction_ of the force of attraction on the needle. But there may be also changes in _intensity_ of this action; the pull may be a little stronger or a little weaker than before, and these variations are not represented by any actual movement of the needle, though they can be measured by proper experiments. We can, however, imagine them represented by a movement of the end of the needle if we suppose it made of elastic material, so that it would lengthen when the force was greater and contract slightly when the force was less. If a pencil were attached to the end of such an elastic needle so as to make a mark on a sheet of paper, and if for a moment we exclude the up and down movements, the pencil would describe during the day a curve on the paper, as the end of the needle swung backwards and forwards with the change in direction, and moved across the direction of swing with the change in intensity. Now when curves of this kind are described for a day in each month of the year, there is a striking difference between the forms of them. During the summer months they are, generally speaking, comparatively large and open, and during the winter months they are small and close. This change in form is seen by a glance at Plate XIII., which gives the curves throughout the whole of one year. Let us now, instead of forming a curve of this kind for each month, form a single average curve for the whole year; and let us further do this for a series of years. (Plate XIV.) We see that the curves change from year to year in a manner very similar to that in which they change from month to month in any particular year, and the law of change is such that in years when there are many sun-spots we get a large open curve similar to those found in the summer, while for years when there are few sun-spots we get small close curves very like those in the winter. Hence we have two definite conclusions suggested: firstly, that the changes of force are sympathetic with the changes in the sun-spots; and secondly, that times of maximum sun-spots correspond to summer, and times of minimum to winter.