Conclusions and recommendations

• The optimal number of grains that should be dated of a detrital provenance sample can be looked up from Table 1, Figure 3, or the web-form [9]. To be 95% certain that no fraction $\geq$0.05 of the population was missed, 117 grains should be dated. This is a fairly large number, often too high perhaps for analytical methods such as fission-track, (U-Th)/He, or TIMS. 117 measurements may be more readily achievable with the ion-microprobe (e.g. [11]) or laser ablation ICP-MS (e.g. [13]).
• If there exists some prior knowledge about the population that indicates it is not uniformly distributed, a risk can be taken to date fewer that the optimal number of grains, by using Figure 5. To be 95% certain that no fraction f$\geq$0.05 was missed, it is recommended that this number be no less than 95. However, dating fewer grains limits the possibility to rigorously calculate and report p and f.
• It is definitely not the purpose of this paper to suggest that studies reporting fewer than 117 single-grain measurements would be scientifically wrong. The purpose of some provenance studies may be to prove the presence of one or more specific age fractions in a detrital population. Once these fractions have been found, there is no reason to date more grains. It is only when provenance studies discuss the absence of certain age fractions that counting statistics come into play. Even then, it may not be possible to date as many as 117 grains for technical, financial or other reasons. If fewer than 117 grains were dated per sample, or when age-histograms must be interpreted from published studies that use fewer than the optimal number of grains, the actual p$_{max}$ and f values that result from using the available number of grain ages should be reported. For example: if only 60 grains were dated, it is sufficient to report that the maximum probability of missing at least one fraction greater than 0.05 is p$_{max}$=64%, or that there is 95% confidence that no fraction f $_{act} \geq$0.085 was missed. Note that the latter definitely sounds better than the former. Such information can be obtained from Equation 4, Figure 3, Table 2, or the web-form [9]. In theory, an alternative solution to changing p and f would be to reduce the number of bins of the age histogram to M$_{opt}$, according to Table 2 or the web-form [9]. However, M$_{opt}$ is typically a low number which would over-smooth the histogram.