## Appendix A
### Remament Magnetization in Ceramic Fractures
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Base Specimen**} & \multicolumn{6}{c}{**Magnetic Field Measurements from the Cylindrical Specimens of Vase 5**} \\ \hline  & \(\varphi_{S}\) (\(\pm\)0.5°) & **0°** & **30°** & **60°** & **90°** & **120°** & **150°** & **180°** & **210°** & **240°** & **270°** & **300°** & **330°** \\ \cline{2-13}  & \(\overline{\mathbf{B}}_{x}\) (\(\pm\)1)nT & 0 & 28 & 51 & 60 & 53 & 31 & 1 & \(-\)31 & \(-\)53 & \(-\)60 & \(-\)53 & \(-\)32 \\ \cline{2-13}  & \(\overline{\mathbf{B}}_{x}\) (\(\pm\)1)nT & 16 & 16 & 17 & 16 & 17 & 16 & 17 & 17 & 16 & 17 & 17 & 17 \\ \cline{2-13}  & \(\overline{\mathbf{B}}\) (\(\pm\)1)nT & 63 & 61 & 62 & 62 & 62 & 62 & 62 & 62 & 62 & 62 & 62 & 62 \\ \cline{2-13}  & \(\overline{\mathbf{\Theta}}\) (\(\pm\)1°) & 75 & 75 & 74 & 75 & 74 & 75 & 74 & 74 & 75 & 74 & 74 & 74 \\ \cline{2-13}  & \(\overline{\mathbf{\varphi}}\) (\(\pm\)1°) & 0 & 28 & 60 & 90 & 118 & 149 & 179 & 211 & 242 & 269 & 298 & 327 \\ \hline \multicolumn{13}{c}{**Column of m tiles**} \\ \hline \multicolumn{13}{c}{**L\({}_{\mathrm{m}}\)(\(\pm\)0.2)mm**} & \(\varphi_{S}\) (\(\pm\)0.5°) & **0°** & **30°** & **60°** & **90°** & **120°** & **150°** & **180°** & **210°** & **240°** & **270°** & **300°** & **330°** \\ \hline \multicolumn{13}{c}{**m**} & \(\overline{\mathbf{B}}_{x}\) (\(\pm\)1)nT & 43 & 37 & 21 & 1 & \(-\)23 & \(-\)39 & \(-\)44 & \(-\)36 & \(-\)20 & \(-\)2 & 21 & 38 \\ \cline{2-13}  & \(\overline{\mathbf{B}}_{x}\) (\(\pm\)1)nT & 0 & 22 & 39 & 43 & 36 & 22 & \(-\)1 & \(-\)23 & \(-\)38 & \(-\)45 & \(-\)38 & \(-\)21 \\ \cline{2-13}  & \(\overline{\mathbf{B}}_{x}\) (\(\pm\)1)nT & 14 & 14 & 14 & 14 & 15 & 15 & 14 & 14 & 14 & 14 & 15 & 15 \\ \cline{2-13}  & \(\overline{\mathbf{B}}\) (\(\pm\)1)nT & 45 & 45 & 46 & 45 & 45 & 47 & 46 & 45 & 45 & 47 & 46 & 46 \\ \cline{2-13}  & \(\overline{\mathbf{\Theta}}\) (\(\pm\)1°) & 72  
The computed angle, \(\tan\varphi=B_{y}/B_{\omega}\), is similar to the measured disk rotation angle (\(\varphi_{S}\)) (Chart A3a), which confirms the measurements from a magnetically isotropic cylindrical area around the \(z\)-axis, which maintains its rotational symmetry during the increase of the column thickness. \(B_{\omega}\), \(B_{y}\), \(B_{z}\) increase at a declining rate and stabilize for a certain column thickness, different for every vase, beyond which the increase of the magnetically detecting region remains outside the sensing range of the sensors. The range and measurement rate of increase of the vertical y-sensor are smaller than those of the parallel x,y-sensors, because their sensitivity is different. The measured thickness, \(L_{m}\)= m.L\({}_{o}\), of each tile column from the vases 4, 5\(\&\) 6 where the magnetic field magnitude B stabilizes (A.4) is approximated geometrically by the column diameter and the sensor readings (Table A5), if it is assumed that the cylindrical ceramic area that generates the magnetic field, which is detected by the sensors, extends along the direction of the field **B** (Figure A8) and the reading of the vertical z-sensor doubles. The magnitude of the magnetic field increases with the increase of the column thickness, \(L_{m}\), (Figure A8b,c) and stabilizes when the inclusion of additional tiles (Figure A8d) does not alter the height, \(\mathbf{\ell}_{m}\), of the cylindrical excitation area of the sensors. Figure A8: For the geometric interpretation (**b–d**) of the results, \(B_{yy}\) is drawn (**a**) in the direction of the x-sensor. Investigation of the Dependence of the Measured Magnetic Field on the Sensor Orientation on the Fragments' Surface. Theoretical Approach of the Cylindrical Magnetically Detected Area by the Sensors  
From the co-belonging base fragments which display similar magnetic field, cylindrical tiles are constructed (Figure 10). With \(\mathrm{B_{xy}}\) oriented at the same direction, a specimen is assembled, with a magnetic field of similar magnitude and directionality and with a diameter equal to its height.