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By N. I. Fisher

This is often the 1st accomplished, but essentially provided, account of statistical tools for analysing round facts. The research of information, within the kind of instructions in house or of positions of issues on a round floor, is needed in lots of contexts within the earth sciences, astrophysics and different fields, but the method required is disseminated during the literature. Statistical research of round information goals to provide a unified and up to date account of those tools for functional use. The emphasis is on purposes instead of idea, with the statistical tools being illustrated through the ebook by way of info examples.

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2). 3) so that (6, ) has direction cosines (x, y, z) = (SJR, Thus Sy/R, SJR). 1 Pu P2, P 3 , P4 and P 5 are points representing_unit vectors in 3-dimensional space, c is the angle between the vectors OPX and OP2. 1. 6) 180°<<£<270° if JC<0, y<0 270°<<£<360°if x > 0 , y<0. (Care is required in programming the exceptional cases x = 0 and y = 0). (0, $) is called the mean direction of the n unit vectors, R the resultant length, and R = R/n the mean resultant length. , Pn (considered as unit masses) has coordinates (Z xi/n-> Z yi/n9 Z zt/n)) in the direction (0, $) at a distance £ from the origin.

A) Wulff, or "stenographic", projection Definition p = tan (90 - \6), i/r = 0, 0 ^ p ^ 1, 0 ^ \[r < 2n. 4. 4 Definition of the equal-angle projection P* of P. 38 3. 3). The Wulff projection is commonly used in engineering work, Crystal Morphology, Palaeomagnetism and Structural Geology. (b) Lambert, or Schmidt, projection Definition p = 2 sin (90-^9), ^ = (f>, 0 ^ p ^ y/2, 0 ^ \jr < 2n. 5. Properties This is an equal-area projection: equal areas on the surface of the sphere map to equal areas on the plane of projection.

N. -=/i + i x ( / * - / i ) / ( f c + l ) , i = l , . - . 31) (b) k values dividing the N/-values into k+\ approximately equal groups (equal probability contours) each of approximately N/(k+\) values; thus Ci =fju),j(i) = nearest integer to {i-\)N/k, i = 1 , . . , k. 10 Regular grid containing points at which the density / is evaluated for choice of contour levels. / V\ >\ \ L\ A A W I A\ / //1 \ / \ *-- \s A \ / / y 44 3. Descriptive and ancillary methods; sampling problems (c) k values dividing the N/-values into /c+1 groups decreasing in size as the /-values increase.

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