## 3 Results and Discussion
### Mass
Both the filling and dimensions of a mill (any tumbling drum) have an impact on its power, which can also be seen in the theoretical equations for the power and introduced energy (mechanical work) estimation (section \"Abrasion Energy Input (Mechanical Work) and Power Estimation\"). Specific mass loss (mass loss per unit of mass per power) data, obtained from both tests, and energy inputs were highly correlated, with R\({}^{2}\) = 0.99 (\(p\)-value \(<\) 0.01) (according to a linear correlation of linearized, log-transformed data) and RHO = 0.99 (\(p\)-value \(<\) 0.01) (according to Spearman rank correlation). Obvious discordance appeared in the last Los Angeles cycle data. This might have been caused by the handling of the material--exaggerated mass loss due to the additional loss of the material, as described in the sections \"Abrasion in Micro-Deval Apparatus\" and \"Abrasion in Los Angeles Machine\". However, if the power decrease was disregarded, that is, if mass loss was considered constant throughout the whole abrasion process (all cycles) in both machines, the datasets overlap slightly better (Figure 7a), although the general function fitted to both datasets did not considerably change. If we observed only the energy input scope with data from both machines (up to about 30 kJ), the same could be noted. The curve fitted to such data (Figure 7b) (with available energy input data for both tests) follows Equation (16). Similar approaches, with expressing community using various machine or process properties (e.g., specific power), are often used in mineral processing, for mill scaling. An example of such an approach can be found in [PERSON] et al. [48], where mass loss was normalised by \"surface specific comminution energy\" to be able to compare the grinding rates obtained by mills with different dimensions, filling, and power. \[ML_{s}=ML*C_{ML} \tag{14}\]  
\[C_{ML}=(P*m_{0})^{-1} \tag{15}\]  
\[ML_{S}=0.1E^{0.85} \tag{16}\]  
where: \(ML_{S}\)--specific mass loss (%/(kg*)); \(ML\)--mass loss (%); E--input energy (mechanical work); \(C_{ML}\)--mass loss coefficient; P--power (W (J/s)); \(m_{0}\)--initial mass of the sample material (kg). Equation (20) was derived (by steps shown in Equations (17)-(19)) from the relation expressed in Equation (16), which was based on experimental data obtained in both micro-Deval and Los Angeles tests, for the input energy scope with available data for both tests. This notation of the relation between the residual mass and the energy inputs is in a form most commonly used for describing the wear of particles (the mass form of Sternberg's law [8]. This relation is presented by fitting curve in Figure 8a. Figure 8b shows measured vs. predicted residual mass (in kg) values (\(y=1x\)). \[100\%-RM\%=0.1E^{0.85}*{C_{ML}}^{-1} \tag{17}\]  
\[RM\%=\frac{m_{0}-m_{res}}{m_{0}}*100 \tag{18}\]  
\[\frac{m_{res}}{m_{0}}=0.35*e^{1.05*(1-\frac{0.1}{100}*E^{0.85}*{C_{ML}}^{-1})} \tag{19}\]  
\[m_{res}=m_{0}*0.35*e^{1.05*(1-\frac{0.1}{100}*E^{0.85}*{C_{ML}}^{-1})} \tag{20}\]  
where: \(RM\%\)--residual mass (\(\%\)); \(m_{res}\)--residual mass (kg). When the expression from Equation (19) was plotted against the input energies, the original relation between the relative residual mass (\(m_{res}/m_{0}\)) and the energy input for each process was obtained (Figure 9), with the general expression following Equation (21) and also Equation (22). Exponent \(c\) is an abrasion coefficient, which is lithology specific, but also seems to be process (power conditions) dependent. The coefficient \(c\) obtained was  
Figure 8: (**a**) Graphical representation of Equation (19) (data from micro-Deval tests are marked blue, and from the Los Angeles tests marked orange), (**b**) measured vs. calculated residual mass using Equation (20). One should note that in Figure (**b**), there are multiple points marked blue (representing data from micro-Deval tests), but they are close to each other.