*5.2. The Horse Bronze Statue from Musei Capitolini, Rome*

In 1894, a number of bronze objects were found in an old cellar in Rome, some of them of great artistic interest. Among them, a beautiful statue of a horse, heavily damaged, was transferred to Musei Capitolini and adequately restored. The statue, see Figure 6, is of natural size and has been exhibited in the Musei since then.

**Figure 6.** Sculpture, bronze horse, (Capitoline Museum, Rome, Italy). Ph credits Di MM -Opera propria, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=22426880, accessed on 31 July 2021.

More than thirty years ago, the statue was submitted to a program of restoration and studies. By the study of the internal clay core, we tried to determine the date of the casting. The problems we faced are presented in Section 4; the expected accuracy could not be very high, either for the material constituent of the clay core, which cannot always be considered a ceramic, or for the difficulties in precisely determining the radiation exposure, due to the uncertainties in the external dose and in the water content. The case of the clay core

from the horse statue was rather favourable, at least as regards the type of the constituent material, which did not present any spurious TL, and the calculation of the total absorbed palaeodose could give a rather low uncertainty and similar results among the three samples taken from the interior of the statue. The palaeodose, as measured applying the "fine-grain technique" resulted as D = 13.2 ± 0.6 Gy and was published in a review book [10]. The dating of the statue could not be determined due to the poor information about the dose rate, but a clear indication of a Greek origin was reached, due to the rather elevated value of palaeodose, whatever the dose rate might be, within reasonable values. In the present re-calculation, new information was added and a more reliable assignment of the casting to the Greek period was reached.

We start from the data already obtained in the first measurements, i.e., the internal dose rate, which turned out to be 3.4 ± 0.3 mGy/a. Furthermore, the reported value must be considered as the maximum value of internal dose rate, because any water content would reduce this value. The measurement of the external dose rate, of course, is one of the main sources of uncertainty, together with the water content in the past, as discussed in Section 4. To try to obtain an acceptable value of external dose rate, a dosimetric measurement of the gamma dose rate in the cellar where the statue was found in 1984 was necessary. This value was 4.1 ± 0.3 mGy/a, once more without taking into account the role of water content [4].

To summarise the external dose rate, the statue was exposed to three different dose rates: the first for an unknown period, t1, until it was abandoned in the cellar where it was found, a second for the period t2 in the cellar and a known third period, t3, in Musei Capitolini.

Therefore, having evaluated the dose rates related to the three periods and the palaeodose, it was possible to calculate the statue age by solving a simple parametric equation:

$$\begin{cases} \text{ T = t\_1 + t\_2 + t\_3 = \frac{D\_1}{d\_1} + \frac{D\_2}{d\_2} + t\_3} \\ \text{ D = D\_1 + D\_2 + D\_3} \end{cases} \tag{2}$$

where T is the age of statue (the dose rates d1, d2 and the period t3 were evaluated) and D is the palaeodose (D3 was calculated).

By solving (2), it is possible to obtain the age of casting of the statue as a function of the unknown period t1:

> -

$$\mathbf{T} = \mathbf{m}\mathbf{t}\_1 + \mathbf{q} \tag{3}$$

where

$$\begin{array}{c} \mathbf{m} = 1 - \frac{\mathbf{d}\_1}{\mathbf{d}\_2} \\ \mathbf{q} = \frac{\mathbf{D} - \mathbf{D}\_3}{\mathbf{d}\_2} + \mathbf{t} \end{array} \tag{4}$$

Figure 7 shows the straight lines obtained in the complete absence of water in the clay cores and with water concentrations varying from 2% to 10%.

Larger percentages are considered unlikely due to the compactness of the material. The intercept of the lines at t1 = 0 provides the age of the horse in the various humidity hypotheses and is the minimum possible in the various cases. The straight line corresponding to 0% water content represents an unrealistic situation but identifies the lower limit of T for the different values of t1. Reasonable values of water content (5–10%) and outdoor periods (100 < t1 < 300 years) lead to the more likely age between about 2300 and 2400 years and, so, assign the casting of the bronze horse to the classical Greek era.

**Figure 7.** Time elapsed since the casting vs. the period of the outdoor location. Different concentrations of water in the burial environment were considered.

## *5.3. The Statue of Saint Peter in the Vatican*

A case in which a clay core behaves almost like a ceramic was found in the analysis of the statue of Saint Peter in the Vatican Basilica in Rome (see Figure 8).

**Figure 8.** Bronze Statue of Saint Peter (Arnolfo Di Cambio, St. Peter's Basilica, Rome, Italy). Ph credits Jordiferrer, CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0, accessed on 31 July 2021>, via Wikimedia Commons.

The clay core found inside the statue was indeed mostly constituted by clay, which gave a very good dosimetric response [11]. All the three measured samples gave repeatable luminescence intensity and a linear response to the artificial irradiation by the radioactive sources in laboratory. It was then possible to obtain values of the palaeodose in a very narrow Gaussian distribution; the obtained value was 2.7 ± 0.2 Gy. The homogeneity of the material inside the statue allowed a precise determination of the radioactivity content of the clay core; then, the internal dose rate turned out to be 3.3 ± 0.1 mGy/a. The compactness of the clay core allowed to reduce to a very low level the effect of the water content; it must be highlighted that it is almost certain that the statue was put where it is now since its making. As a further consequence, the external dose could be evaluated, taking in due account

the attenuation of the bronze itself. All that considered, the annual dose rate resulted to be 3.9 ± 0.2 mGy/a, whose value put in the age equation gave 680 ± 60 years, hence determining a date for the casting of the statue at the beginning of the XIV century. This is in good agreement with the proposal of scholars who attribute it to Arnolfo di Cambio. The dating of this statue is a particularly favourable case of dating clay core taken from the inside of a bronze statue. This is evidently due to the good quality of the clay core itself, in the sense that it was a material very similar to a ceramic, and to the utmost importance of the possibility of determining all the variables contributing to the radiation dose rate, that, in the case of a statue very likely to have been always in the same environment, can all be determined with good precision.
