From here on, all line-force parameters derived from a given or calculated force itself will be denoted with an additional circumflex, in contrast to those parameters related or resulting from a specific line statistics.

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The same result can be found by applying definition (26) to our alternative expression for the line acceleration (21), again independent from any assumption for the line statistics. Note also, that Gayley ([1995]) defined the effective $\alpha$ value at the critical point by the same expression.

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... balance

So far, we have not been concerned with $\hat \delta$ . Before discussing this quantity in Sect. 4.1, we anticipate that the variation of $n_{\rm e}/W$ (for given t) leads to a variation in total line number $\propto N_{\rm o}$ , which can be described by $N_{\rm o} (n_{\rm e11}/W)^{\hat \delta}$ .

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... field

We note that the inclusion or neglect of the very strong, however somewhat peculiar (Sect. 4.2.6) hydrogen Lyman lines does not affect the discussed discrepancy.

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... hydrogen

If H I is a trace ion.

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... number

Under very specific conditions, the effective $\hat \delta$ can even become negative.

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... $\gamma$

A likewise agreement has been found for simulations at T = 5000 and 10000 K.

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...)

The argument given here remains also valid for flux-weighted distribution functions, which are the actual basis for deriving force-multipliers.

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... outside

Only for the CAK velocity law with exponent $\beta = 0.5$ this value remains constant, whereas the inclusion of the "finite disk correction factor (Friend & Abbott [1986]; PPK) as well as the observations (Puls et al. [1996]) give considerably larger values $\beta = 0.8\ldots 1.3$ .

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... $\alpha(k_{\rm L})$

Actually, $\alpha$ is not the local slope itself, however $\alpha = 1 - s$ , if s is the negative exponent of the according cumulative distribution function.

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... ions

After this study has been finished, we received a preprint by Vink et al. ([1999]) who have investigated the so-called bi-stability jump in hot star winds. By calculating the force-multipliers in a way similar to our approach, they reached the same conclusions concerning the relative importance of iron group elements vs. light ions with respect to ${\dot M}$ and $v_{\infty}$ .

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