...radii of the two circles, d is the distance between their centers, and tJAa k=—.. . *---.^==i = s1n 7 /•"and E are the complete elliptic integrals of the first and second kind, respectively, to modulus k. Their values may be obtained from the tables of Legendre, or the values of Mt- \irJAa may...

...where and .• in the expression for V b+b' , . .. . , ., f=— — — c 1n the express1on for Vl F and E are the complete elliptic integrals of the first and second kinds respectively, to modulus £, where *«=-. and ^"(y) are the incomplete elliptic integrals...

...where (34) and where and c= in the expression for V b+b' , c=- — — c' i in the expression for Vl F and E are the complete elliptic integrals of the first and second kinds respectively, to modulus £, where __ -« 'T and ^(y) are the incomplete elliptic integrals...

...r? \n. — a.— 'ia cos* 7 + 8«, cos* 7! o. jg L 1 <J !« / ' -! *J 800" cos' 7 = — j — -j-4 and F and E are the complete elliptic integrals of the first and second kinds with modulus k = sin 7. When the coils have equal breadth £, = £,= £ and a^ = £',...

...(5-5), *here A is an arbitrary constant and 2 .'o"1 cos2<f>d<j> Jy sin2 <f> (5-51) (5-52), K and E being the complete elliptic integrals of the first and second kind respectively to the modulus sin Jy. By considering the integral in equation (5-51) we can show that r/X or y' steadily increases...

...cases n=0 and n= 1 (44) shows that = ¿K(p) (45) 4¿¿(p) ¿ 1)K(¿) _¿E(p)} (46) where K(j4 and E(p) are the complete elliptic integrals of the first and second kind, respectively, whose modulus is p. Another useful relation derivable from (42) and (43) is 1 M =(¿+¿){ ¿ +(3—...

...values of Hx and H, are given by the equations: ~D\_(kl> +lz)E(kl') +(k*' +ft)E(k*)J (24) (25) where K and E are the complete elliptic integrals of the first and second kind, respectively, to the indicated moduli. (26) 16D(Dt) (27) Equation 23 was obtained as follows. Let H denote the magnetic...

...between their planes we have M = 4ir(Aa)1«[(2/* — A)F — (2/*)E], where A=2(Aa)W/[(A-|-a)»+d»]i/», and F and E are the complete elliptic integrals of the first and second kind respectively. If we write, <? + d? = r*, we get from the theory of elliptic functions M = 4jra[log (8a/r) . P —...

...vortex-filament of indefinitely small section, putting adydc—m^ and the corresponding part of ^ = ^,ni, we have and F and E are the complete elliptic integrals of the first and second orders for the modulus K. If we put, for sake of brevity, U=?(FE)-*F, where, therefore, U is...

...0.8 >.O 1.2 (d) where x = \u\/Ug, z' = (1 - x 2)1/2, ug is the gap frequency (2.10) and K(x) and E(x) are the complete elliptic integrals of the first and second kind, respectively (see, eg, Reference 1.41). Real parts of the functions Ip q(U) are always even and the imaginary parts...