The distances marked in the third column are used as radii of the circles drawn round the places to which they respectively refer. The centre of the circle drawn to touch the circles of the first column, and at the same time to pass through Huanillos, is marked C. The position from which the shock originated appears therefore to have occurred very near to a place lying in Long. 7° 15′ W. and Lat. 21° 22′ S. [Illustration: FIG. 31.] The actual operations which were gone through in making the accompanying map were as follows. First, the places with which we had to deal were represented on a map in orthographical projection, the centre of projection being near to the centre of the map. This was done so that the measurements which were made upon the map might be more correct than those we should obtain from an ordinary chart where this portion of the world was not the centre of projection. Next, a number was taken as equal to the velocity with which the sea wave had travelled. The first velocity taken was about 400 feet per second—this being about the velocity with which, theoretically, it must have travelled in an ocean having a depth equal to that indicated upon the charts—also it seemed to have travelled at this rate from the various times of arrival as recorded at places along the coast. Circles were then drawn round Tocopilla, Cobija, Iquique, and Mejillones with radii equal to 2, 8, 10, and 15, each multiplied by (60 × 400). It was then seen _by trial_ that it was impossible to draw a single circle which should touch four circles and also pass through Huanillos. These four circles were, in fact, too large. Four new but smaller circles, which are shown in the map, were next drawn, their radii being respectively equal to the numbers 2, 8, 10, and 16, each multiplied by (60 × 350), and it was found that a circle, with a centre C, could be drawn which would practically touch the four circles, and at the same time would pass through Huanillos.