Conversions of distances, in the course of a text are well not very evocative. We prefer a semigraphic representation, more ordered (table), allowing a total visualization of the problem. One will examine each couple of values to seek the obvious agreements, which will immediately provide an indication of the module of distance used. The discordances in the unit selected will be analyzed and several assumptions will be tested. If one of these assumptions is appropriate, the value of the module will be generalized in order to define reports/ratios of distances for the ancient points not yet identified with a modern locality.

How to determine the distance actually taken into account by the creators of the demarcation of the ways? It was a distance between cities, of gate with gate. But what happen did crossings of the boroughs, rivers? The round numbers were always obtained by round-offs or well sometimes, by truncation? By where passed the ancient way, so badly defined in the areas with the tormented relief? Only the study of the regional monographs will make it possible to find trace of such or such undeniable testimony.

The cartographic support 1/25 000 is perfect for curvimetric measurements, but the handling of a great number of cards (more than 200 for the zone considered) is not easy thing (without evoking the costs). The scale of the 1/50 000 becomes more pleasant to use, while preserving an excellent precision. The 1/100 000 constitutes practically the last highly reliable scale (while starting to require corrections because of cartographic smoothing ). This map has the advantage of providing information of distance, even on the smallroads (it will also be advisable to correct them since they are measured of centre town in the centre town!). Despite everything these imperfections, these measurements of distances end up being statistically highly reliable and it is by multiplying the examples of applications that one will be able to lead to a quasi-certainty on their validity.

The checking on the ground can be carried out by using average the modern techniques: laser telemeter and especially receiver of satellites GPS . This last system makes it possible to follow, even conveys some, the small roads and paths of culture which often cover the way and to record instantaneously the position of all the remarkable points and that with a precision of about fifteen meters, even on several tens of kilometers.

Application to the inscriptions of the milliary columns.

We retained some examples of regional milestones carrying multiple indications of distance, facilitating a better evaluation of the module used. The objection " the milestones ones are not in place " is often formulated. It is true, and it is the reason of the choice of these milestone so that a possible trigonometrical triangulation makes it possible to determine (or simply to confirm) the initial localization. If milestone carrying only two inscriptions, is placed on an undeniable way (case of milestones of Rom, evoked below), it is even simpler since the sum of the indications generally gives the distance civitas - fine , allowing to determine the metric employee easily, therefore the initial position of the terminal.

The first application relates to the inscription of the milestone of Moutiers d' Ahun, Creuse. (C.I.L. N° 8911). This milestone bear two indications of distances: PR XX and L XXXIII . According to A. Grenier, these mentions correspond to St Goussaud and Limoges. A.Grenier, page 90 (Bib.). Routes suggested: