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. 1918 Excerpt: ...transformation reversed gives a smaller modulus and an increased amplitude. In this case if k be the new modulus and k the old, we have and for the amplitude, tan ($, -) = (1-P) tan f...................................... (8) It is to be noticed that if the amplitude $ = fyrr, the new amplitude ti = Tr. The amplitude, ...
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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. 1918 Excerpt: ...transformation reversed gives a smaller modulus and an increased amplitude. In this case if k be the new modulus and k the old, we have and for the amplitude, tan ($, -) = (1-P) tan f...................................... (8) It is to be noticed that if the amplitude $ = fyrr, the new amplitude ti = Tr. The amplitude, will then be 2ir, and so on to n = 2"( jr). Now we obtain by repetition of the transformation, IP/I JL "EV7.-J I t (-!, ) =--r-r-r (An, pn;, 12-,"!-oo) where l]O-AJ., )4 Here the limit n (71=00) is zero, and therefore If the complete elliptic integral is required, we have 4/2" = Jtt, and therefore K(k)= Lt(l +AOO +, )...(l+ n) (12) By means of the last result the complete elliptic integral of the first kind for a given modulus k can be quickly determined. For example, if = 0'5 ( = sin 30), we obtain /fc, =0-0718, &, = 0-00129. Using only these we obtain K() = l'07309 = 1'686-e, (13) where O'OOOa e O'OOOl. Again let =v/3/2 ( = sin 60). We find at once i = J k = 1-2%/2=0-029438, k3=0-000216, which give K) = 2'167-, (14) where 0-0005 e 0-0001. 9. Convergent series for elliptic integrals of first and second kinds. Other formulae of calculation for K and E have been developed. We give here a useful process for K. A similar process is also applicable to E. Let P, Pj, P2, ... be defined by the equations The values of P, P, P2, ... are first calculated, and the value of K is then obtained by the equation just written. It will be observed that when the terms necessary for P have been evaluated, the proper procedure is as follows. Let us suppose that the term (1.3.5)/(2.4.6)V2 ia the smallest which it has been thought necessary to include: then that is set down as P3. To that is added...
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PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
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PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
