By D. W. G. Ballentyne B.Sc., Ph.D., F.Inst.P., D. R. Lovett M.Sc., A.R.C.S., D.I.C., Ph.D., M.Inst.P. (auth.)

The layout of this variation continues to be unchanged from earlier variants however the majority of entries have obtained a few revision. particularly, devices at the moment are in SI devices at any place attainable, even supposing with yes of the classical entries this isn't attainable. Chemical terminology has proved a selected challenge. we now have stored the typical names for natural compounds a result of large readership of this publication yet we now have additional an additional desk giving the an identical systematic names and the formulae. we've got attempted to prevent omission of any named results and legislation that experience extensive utilization. however, which will preserve the publication to a workable size, it's been essential to make a choice one of the much less prevalent phrases and it really is inevitable that a few arbitrary offerings and omissions has to be made. a few entries from past versions were omitted to make room for different entries which we consider became extra very important. we're particularly thankful to these readers who've mentioned earlier omissions. D.W.G.B. Imperial university, Uni!.:ersity of London D.R.L.

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Burgers'Vector The vector necessary to close Burgers' Circuit. It is at right angles to the dislocation for a pure edge dislocation and parallel to the dislocation for a screw dislocation. & {f(a, 0)+ f(O, a) + f( - a, 0) + f(O, - a)} -I -I + 19{ f(b, b) + f(b, -b) + f( - b, b) +f(-b,-b)} 45 Burnside's Theorem where a = most. J~ and f(x, y) is a polynomial of degree 5 at Burnside's Theorem The necessary and sufficient condition that an n-dimensional representation OrR) be an irreducible representation of a group is that there exist n 2 linearly independent matrices in set {O(R)}.

Chladni's Figures Patterns set up by sprinkling sand upon a glass plate which is set vibrating with a bow. The plate is supported centrally and different symmetrical patterns are obtained by gripping one edge of the plate

An)/1l --+ a. and an > 0, then an) I in --+ a. X then there exists a point c such that a < c < b where fIb) -f(a) f(c) ¢(b) - ¢(a) ¢'(c) 51 Cauchy's Rule for Series Cauchy's Rule for Series provided the three series are convergent. Cauchy's Tests for Convergence (1) In 00 I Un = n= 1 UI + U2 + if lim IUn II in < 1 n~x LU n is absolutely convergent. (2) Iff(x) be a steadily decreasing positive function such that f(n) ? an, then Lan is convergent if Ioc f(x)dx is convergent. Cauchy's Theorem (for a Square Matrix) The adjugate of a square matrix is that matrix whose (i,j)th element is the cofactor of the U, i)th element in IA I, the determinant of A; the cofactor is ( _l)i+ j multiplied by the minor, and the minor is formed from the square matrix A by suppressing the ith row andjth column.