World-life; or, Comparative geology . Fig. 39. —Film Tide. 228 A COOLIKG PLANET. is spread over a circular area of about one-fourth theextent. Each circular area, nevertheless, is more than aquadrant in breadth, having a radius, in a homogeneousspheroid, of 54° 44. The tidal effect on the same tide-bearer, is directly asthe mass of the tide-producer, and inversely as the cube ofits distance. But for any other tide-bearer, the effect isalso proportional to its radius.* These principles result from the following reasoning:C. Fig. 40.—Quaxtitativb Relations of Tides, Let D = E M (Figure 40)= dist
World-life; or, Comparative geology . Fig. 39. —Film Tide. 228 A COOLIKG PLANET. is spread over a circular area of about one-fourth theextent. Each circular area, nevertheless, is more than aquadrant in breadth, having a radius, in a homogeneousspheroid, of 54° 44. The tidal effect on the same tide-bearer, is directly asthe mass of the tide-producer, and inversely as the cube ofits distance. But for any other tide-bearer, the effect isalso proportional to its radius.* These principles result from the following reasoning:C. Fig. 40.—Quaxtitativb Relations of Tides, Let D = E M (Figure 40)= distance between centres of tide-bearer and tideproducer, m — mass of tide-producer,E = E B = radius of the attractions at B, E and A are expressed bym(D-R)2 Subtracting the second from the first, and the third from the second, weget, very nearly, K)2 Excess of attraction at B over E; Excess of attraction at E over A. 2wR 2 m R 1)3 But the latter is actually a little less than the former. TliL^e expressions show that the efficiency of the tidal force of the same tide-producer vurits dlrecly as the radius of (he tide-bearer and inversely as the cubeof (he distance of (he tide-producer. Now, further, if we assume any point P, on the surface of the tide-bearer,at the angular distance from the line E M, joining the centres, and put {/for in-tensity of gravity on tide-bearer, and p for the relative density of a thin externalfilm covering a rigid nucleus, then the elevation (or depression) of P
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Keywords: ., bookcentury1800, bookdecade1880, bookpublisherchica, bookyear1883
