July, 1887.] ELLIOTT -SOCIETY. 169 



to A, and in direction more and more nearly horizontal. Tlie intensity of the 

 disturbance at the surface in the direction of these lines OK, OH, &c., to OA, 

 will be greatest at K, and diminish, and become successively less at H, F, &c., 

 to A, according to some law depending on the distance of each of these points 

 from 0. 



2. We may first suppose the law to be this : the intensity diminishes as the 

 distance increases, so that, at double the distance, the intensity is reduced to 

 one-half, at a triple distance to one-thu'd its intensity at K ; at half the dis- 

 tance it is twice as great, and so on. Expressed mathematically, the intensity 

 is said to be inversely as the distance, or the distance multiplied by the intensity 

 is a constant quantity. 



3. If now we take OK to represent the intensity at K and on OK describe 

 the semicircle Oa, b, &c. , K, it v,nll cut off on the lines O A, OB, &c. , OK, the 

 lines Oa, Ob, &c. , OK, which will represent respectively, the intensities at A, 

 B, &c., K, on the same scale as that on which OK represents the intensity at 

 K. For the triangles AKO, and KaO ( the line K« is not drawn in the figure ), 

 have a common angle at O, and a right angle at K and a. respectively. They 

 are therefore similar, and OA : OK:: KO : 0.^, or 0(2XOA=OK2= a constant 

 quantity. So 0^X0 3=0 K2 and so on ; which agTees with the law above sup- 

 posed. It is also evident that Oa : Ob:: OB : OA, that is the lines Oa and Ob 

 *are inversely proportional to the corresponding distances OA and OB, which 

 is the same law a little differently expressed. 



4. But as already said these forces act at A, B, &c. , along the hues O A, OB, 

 &c., obliquely to the surface, and produce effects partly in a vertical direction 

 and partly in a horizontal one. To find these effects at A we must resolve the 

 force Oa into the two OP and Va ; the first OP shows the direction of the up- 

 ward force at A, and its intensity ( on same scale as before ), the second Fa, 

 shows the direction and intensity of the horizontal disturbance at A. In like 

 manner ON and N& show the direction and intensity of the upward and hori- 

 zontal disturbances at B ; OM and Mc at C, and so on. By comparing the 

 lines OP, ON, and OM, &c., it will be seen that the upward force increases 

 steadily from A to K, where it is greatest, or has its maximum. In like man- 

 ner comparing the lines P«, N&, Mc, L/, Ih, which represent the intensities of 

 the horizontal disturbance at the points A, B, C, F, and H, it will be seen that 

 the greatest of these is Mc, and that the intensity of this force increases fi'om 

 A to C, that there it attains its maximum and decreases thence to F, H, and K, 

 at which last point it disappears entirely, the whole distm'bing force being here 

 exerted entirely upward and vertically. By the properties of the cu-cle the 

 line Mc is equal MO, and therefore KO is equal to KO, that is, the distance of 

 the point of maximum liorizontal disturbance on tJie earth from tJie point K on 

 tlie surface, vertically over tJie focus of disturbance, is equal to tlie depth of that 

 focus of disturbance O beneath the point K. This point K is the centre of the 

 circle that passes through all the points of maximum horizontal intensity on 

 the sm-face of the earth, and KG is radius of that circle and the centre K may 

 be found geomeirically if three or more such points be given on the surface. 



VOL. II. 22 rub'ished Feb., 188S. 



