This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1826 Excerpt: ... y the axis of the spheroid And, as this point is within the spheroid whose semi-axes are and 7, its attraction towards the axis, by (19), hence, its attraction in the direction of x And, by (19), its attraction in the direction of z 4 e 1. 7 5--sy++Av Substituting these, we find, at length, the attraction of A in the ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1826 Excerpt: ... y the axis of the spheroid And, as this point is within the spheroid whose semi-axes are and 7, its attraction towards the axis, by (19), hence, its attraction in the direction of x And, by (19), its attraction in the direction of z 4 e 1. 7 5--sy++Av Substituting these, we find, at length, the attraction of A in the direction of x = L c3 ( __ c'(iaA'-3/'-3g) 3 P'(/V+A')n1+2e ' 5(/'+g + A8)2 F5 that in the direction of y-1 c3 f c(lgft'-3/--3g) that in the direction of z 48.. Prop. 22. To find the attraction of an oblate spheroid on a point without it; the spheroid being heterogeneous; and. all the surfaces passing through points at which the density is the same, being spheroidal, of variable ellipticity. Let EF, (fig. 15.) be the spheroid; let E'F' be a spheroidal surface, at every one of whose points the density is the same, and E"F" a spheroidal surface very near the former, of different ellipticity, at all of whose points the density is the same, bu$ differing from that at the surface E'F'. Let CF=c, CF'=c+Sc. Since the ellipticity varies when the semi-axis of the spheroid is varied, e must be a function of c. Now the density of all the matter included between E'F' and E"F" is not uniform; but by diminishing $c, -it may be made to approximate as nearly as we please to uniformity. Conceive, now, for the moment, the interior matter of the spheroid E'F' to be of the same density as that at its surface, or to be equal to p; let its attraction in the direction of x = p. A. Then the attraction of the spheroid E'F" in the same direction, will be the value which 'receives when c+Sc is put for c, and when, instead of e we put the value of the ellipticity in the spheroid E"F." But if we consider e as a function of c, this ...
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New in New jacket. Mathematical Tracts On Physical Astronomy, the Figure of the Earth, Precession and Mutation, and the Calculus of Variations (Paperback or Softback)
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