A recent paper showed that in the well-known relation I = f(V_{a}+μV_{g}), the parameter μ (commonly called the ‘amplification factor’) should be a constant, and thus independent of the magnitude of I. Though long experience has shown that μ is substantially independent of I, yet the derivation, used in that paper, for calculating the value of μ, appeared to show that it ought to be completely independent of I. The classic derivation of μ, e.g. that used by H.J. Van der Bijl, appeared to show that the classic formula for μ was exact only in the limit when I was vanishingly small.This paper describes measurements designed to test whether really is independent of I. A balance method was devised which was capable of measuring μ to an accuracy of about 1%. The valve which was tested consisted of a separately heated disc cathode, 8 mm diameter and an anode (also 8 mm in diameter) 0.55 mm distant from it. The distance between the grid plane and the cathode was 0.15 mm.Fig. 3 shows the measured values of μ plotted as a function of V_{g} three different constant values of anode current. It shows that, for a given value of V_{g}, μ, in fact, increases by some 20% as I increased from 3 to 11 mA. It also shows that, in fact, μ decreases by about 20% when I is constant, as the negative value of V_{g} is increased from about 2 to 8 volts.Fig. 4 shows that, for constant I, the effect of changing V_{g} is removed by a substantial reduction of cathode temperature; but this reduction does not remove the increase of μ with increase of I. This means that the increase of μ with I is due to the increase of distance between grid-plane and barrier—an increase which must be significant for a valve in which the distance between grid plane and cathode is only 0.15 mm. It is argued, it is thought conclusively, that the effect of V_{g} is due the periodic fluctuations, across the plane of the barrier, of the current density crossing it. The author is convinced that, if a valve had been used in which the pitch of the grid wires was small compared with their distance from the barrier plane, μ would be independent of both I and V_{g}. In other words, μ was constant in the early separately-heated cathode valves.Section 5 points out that the necessary and sufficient condition for constant anode current is that any change in V_{g} must not cause any change in the positive charge on the cathode. Accordingly the positive charge, extracted from the grid to make it more negative, must be handed on, unchanged, to the anode, thereby increasing its potential. If the electric force due to the space charge between grid and anode is ignored as unimportant, and it is shown that this must be true, μ is equal to the product of the capacitance between grid and anode and the capacitance between grid and the barrier plane, both in the absence of space charge—a form which has long been known but whose meaning has always seemed rather obscure. Its validity depends only on (a) ignoring any striation in the stream of anode current, and (b) ignoring the effect of the presence of space charge between grid plane and anode.Section 6 explores the dependence of μ on the ratio of peak gridswing to mean grid potential. Experiment shows that μ is constant, within about 1%, for all peak grid swings which do not exceed the grid bias.