A similar rapid and then gradual decline in frequency characterises the strong and weak shocks recorded at Gifu. Of the ten violent shocks, only one occurred after the beginning of January 1892; and of the 97 strong shocks, only three after April 1892. But at the commencement of the series, feeble shocks (_i.e._, shocks that could just be felt) and earth-sounds without any accompanying movement were comparatively rare, and did not become really prominent until two months had elapsed. Of the 308 after-shocks recorded in 1893, none could be described as strong, only 10 were weak, while 263 were feeble shocks and 35 merely earth-sounds. The last two diagrams show at a glance that the decline in frequency of after-shocks is very far from being uniform. Some of the fluctuations are due to the occurrence of exceptionally strong shocks, each of which is followed by its own minor train of after-shocks.[58] Others seem to be periodic, and possibly owe their origin to external causes unconnected with the earthquake.[59] _Method of representing the Distribution of After-shocks in Space._--The maps in Figs. 54-57 show the distribution of the after-shocks in space during four successive intervals of two months each. They are founded on Professor Milne's great catalogue of Japanese earthquakes, which give, among other data, the time of occurrence and the position of the epicentre for every shock until the end of 1892. For the latter purpose, the whole country is divided by north-south and east-west lines into numbered rectangles, each one-sixth of a degree in length and breadth; and the position of an epicentre is denoted by the number of the rectangle in which it occurs. The area included within the maps is bounded by the parallels 34° 40' and 36° 20' lat. N., and by the meridians 2° 10' and 3° 50' long. W. of Tokio, so that ten rectangles adjoin each side of the map. The number of epicentres lying within each rectangle having been counted, curves are then drawn through the centres of all rectangles containing the same number of epicentres, or through points which divide the line joining the centres of two rectangles in the proper proportion. Taking, for example, the curve marked 5, if the numbers in two consecutive rectangles are 3 and 7, the curve bisects the line joining their centres; if the numbers are 1 and 6, the line joining their centres is divided into five equal parts, and the curve passes through the first point of division reckoned from the centre of the rectangle in which six epicentres are found. Thus the meaning of the curve marked, say, 5 may be stated as follows:--If any point in the curve be imagined as the centre of a rectangle whose sides are directed north-south and east-west, and are respectively one-sixth of a degree of latitude and longitude in length; then the number of epicentres within this rectangle is at the rate of 5 for the time considered.