propagation assumed is 50 miles per minute, and this solution agrees also with Wanganui (8·4), and Westport (8·3) nearly, and is only ¼min. out for Picton (8·2). (y) The method of co-ordinates: The times in the list (a)—all verified by New Zealand Mean Time, and apparently good times, referring to the same phase of the same shock—were employed. Christchurch was taken as the origin of co-ordinates, the line Christchurch-Hokitika as the axis of y, and the axis of x at right angles (north-easterly). The reduced equations are— Opunake), 544x + 196y + ¼u - ½w = 83,588 Kaikoura), 186x - 8y + 9/4u - 3/2w = 8,665 Wellington), 384x - 16y + 9/4u - 3/2w = 36,928 Nelson), 300x + 110y + 9u - 3w = 25,525 Hence x = 145·15 miles, y = 59·6 miles, v = 493/4 miles per minute = 4,378ft. per second (velocity of propagation), and the time at the origin = 8h. 1min. 20sec. A.M. The point K near F, five miles and a half W.S.W. of Nelson, is the point thus found for the epicentrum. By trial we find that a depth of about 5 miles for the centrum best suits the data. This agrees within the limits of errors of observation with Westport, and also with Wanganui, if we take the mean of the two observations (both by good observers). The degree of agreement is shown by the time at the origin as calculated back from each place; it should be the same, of course, from whatever place we reckon. Time at Place of Observation. Time at Origin below K, in Minutes and Decimals. Christchurch 8·41/2 1·35min.past 8. Kaikoura 8·3 1·32" Wellington 8·3 1·32" Nelson 8·11/2 1·33" Opunake 8·4 1·33" — — — Westport 8·3 1·21min.past 8. Wanganui 8·4 1·20" Picton 8·2 (not checked) 0·88" The other places do not give a time at the origin agreeing with this; but the errors are all (or very nearly all) of one sign, and vary from-1min. to - 3·96min., occurring in groups. Examination of the several groups leads us to suppose that there were several shocks, all nearly below K, the first deep, about 25 miles down, the second higher up, and the third about 5 miles below the surface. At some of the more distant