...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 (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...

...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...

...GROVER. 1HE force between two parallel coaxial circular currents was given by Maxwell1 in the form where A and a are the radii of the two circles, z...and second kind respectively, to the modulus k = sin f = </(A + o)1 + z1 Only for circles of equal radii is the force a maximum when the circles are in...

...a are the radii of the two circles, d is the distance between their centers, and k = + a)2 + sin 7. F and E are the complete elliptic integrals of the first and second kind, respectively, to modulus k. He also obtained an expression for the mutual inductance between coaxial circles in the...

...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 —...