The London, Edinburgh and Dublin philosophical magazine and journal of science . hat are producedper per second in the gas as a result of the disintegrationof the emanation. Let n be the number of deposit particles present per inthe gas at a region distant r from the axis. Let D be the coefficient of diffusion of the depositparticles. Then, if there be no applied electric field, we will have,using cylindrical coordinates, as the equation for the steadystate 1 dn\ D -J-V+ —— )=— q \a? r ar ] ± The solution of (1) is given by w=«-^r2+C1logr + CSl (1) (?) where (Ji and C2 have ye
The London, Edinburgh and Dublin philosophical magazine and journal of science . hat are producedper per second in the gas as a result of the disintegrationof the emanation. Let n be the number of deposit particles present per inthe gas at a region distant r from the axis. Let D be the coefficient of diffusion of the depositparticles. Then, if there be no applied electric field, we will have,using cylindrical coordinates, as the equation for the steadystate 1 dn\ D -J-V+ —— )=— q \a? r ar ] ± The solution of (1) is given by w=«-^r2+C1logr + CSl (1) (?) where (Ji and C2 have yet to be determined. Inasmuch as the deposit particles adhere to the exposedsolid surfaces, the concentration in the gas will be zero in thevicinity of the metal, i. t. n = 0 for r = a and r = b. 2E 2 420 Prof. E. M. Wellisch : Experiments on We deduce n _ 9 b2-a + 1_ V-a* Wr, 9 g8loga-68loga4D + 4=Dlog&-loga 10° r+4D log6-loga riff. Inasmuch as the concentration is zero at r = a and r=b, itis obvious that there must be a position rx where the concen-tration is a maximum. By differentiating (3) with respect to r we find r{ 21og- In the steady state the deposit particles may be regardedas streaming towards the central rod or the case according asthey are situated within or without the cylinder r = rx (fig. 1). The relative distribution on central rod and case will thenbe proportional to the volumes cut off by the cylinder r = rij activity on central rod tt^2—- a2)total activity tt(62- 1 2 log a2) h b2-a2 (4> the Active Deposit of Radium. 421 The first term, which in most cases is the more important,is the same as the electrical capacity per unit length of thecondenser. By integrating equation (3) the total number of depositparticles in the gas which are present in the steady state inthe volume corresponding to a height I of the condenser isseen to be
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Keywords: ., bookcentury1800, bookdecade1840, booksubjectscience, bookyear1840
