M. Járó - L. Költő szerk.: Archaeometrical research in Hungary (Budapest, 1988)
Analysis - ÓVÁRI Ferenc: On the metrology of antoniniani originating in the 3rd century
Loss of mass could have occured even if it cannot be observed visually. The spongy texture of the surface of coins can be detected by metallographic methods, selective corrosion can be proved by chemical analysis. The true original mass of coins cannot be extrapolated by virtue of the facts mentioned above. The mass data from the original publications are used. Let us assign the mass of coins belonging to a certain group (sample, determined in the following) as Xj , x 2 , x 3 , jt_. The arithmetic mean can be calculated by the equation: n x=_( Xl + x 2 + x 3 + ...xj= 1 2 Xj (1) i=l where n is the number of coins in the group chosen. The different groups can be characterized by this arithmetic mean. The treatment and comparison of these characteristic numbers are simple and also necessary in the further examinations. The coins belonging to a group can be characterized by the standard deviation [6] too, which can be calculated as follows [13] : a = (Xi-x) 2 • (x 2 -X) 2 • .,. • (x n - x) 2 (2) By the mass distribution of a great number of coins with different mass we mean as follows: Size the mass data of the coins belonging to a group arbitrarily chosen beginning with the smallest and ending with the largest; then divide the data series into arbitrarily chosen but equal intervals (e.g. 0.1 g); name the number of coins in one interval: frequency of distribution. Obviously the number in the group of average mass will be larger than in the groups far from the average. It is clear that the number of jghtest and heaviest coins will be small and the number of average coins large. The distribution function shows this relation. If the intervals are decreased infinitely and a great deal of data are used a bell-shaped curve will be gren. This is the Gaussian or normal distribution and the function can be expressed in the equation: f(x) = \= r ex P (3) where ir is the Ludolphian number x the distance on the x-axis o the standard deviation Different distribution curves can be produced by plotting frequency versus mass of coins from different hoards (Fig. 1). These distribution curves are introduced in the following where the samples are selected according to the families of emperors Figs. 2 and 3 (e.g. the coins of Philip 1. Otacilia and Philip II form one sample). For easier understanding, the covering curve is drawn instead of the column diagram. The three larger hoards referred to in the sounces i.e. of Smyrna, Singidunum and Tulln, are treated separately and all the others are in a single group. Well determined and completely unambiguous (but not too many) groups must be formed for clear treatment. The most simple is to collect the mass of coins according to the emperors independently from the mints and hoards. In this case the distribution functions would be very simple
