## 3 Results and Discussion
### Biochemical Measurement
In turn, the total content of the tocopherols in eggs F was 84 ug/g, and in eggs C was 8% higher at 91 ug/g (Table 2). Analyzing the qualitative composition of individual tocopherols, it was noticed that the content of \(\alpha\)-tocopherol was higher (by 15%) in eggs from caged hens compared to eggs from free-range hens. In contrast, the sum of \(\beta\) and \(\gamma\) tocopherol was 3 times higher, and \(\delta\)-tocopherol 2.7 higher in F eggs in comparison to C eggs. It was found that the proportion of red (a*) in egg yolk F was higher by 13% compared to egg yolk C. Similarly, in the case of the yellow color in egg yolks from free range hens, a 12% higher parameter b* was observed in comparison to egg yolks from caged hens. There were no significant differences in the psychometric brightness (L*) between the egg yolks C and F.  
In the present study, the higher share of yellow (a*) and red (b*) confirmed the higher content of lutein and the sum of carotenoids in the egg yolk from free-range layers. Because yolk color is significantly influenced by the content and ratio of lutein to zeaxanthin, which in the case of eggs F was 8:1, respectively, and in the case of eggs C was 1.3:1 (Table 3).The higher proportion of lutein affects the color and shades it in the yellow-orange direction, allowing it to obtain pigmentation on the La Roche scale, and 9-10 (points). With a higher content of zeaxanthin, the yolk would be more stained, and on the La Roche scale and YCF scale, pigmentation could be obtained up to 11 points. Carotenoid dyes (including \(\beta\)-carotene, lutein, and zeaxanthin) and tocopherols are among the most important hydrophobic antioxidants. Some carotenoids strengthen the immune system of the body and are perceived to be important compounds of pro-health significance. Carotenoids are characterized by high activity against reactive oxygen species as well as free radicals. In addition, a diet rich in lutein helps to prevent the development of cataracts and macular degeneration. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multicolumn{4}{c}{**Carotenoids**} & \multirow{2}{*}{**Total**} \\ \cline{2-2} \cline{4-5}  & **Unknown Pigment** & & & **Lueian** & \(\beta\)**-Carotene** \\ \hline Eggs F & 0.7 \(\pm\) 0.1 & 34.2 \({}^{\text{a}}\)\(\pm\) 1.3 & 4.3 \({}^{\text{a}}\)\(\pm\) 0.1 & nd & 39.1 \({}^{\text{a}}\)\(\pm\) 1.4 \\ Eggs C & nd & 5.7 \({}^{\text{b}}\)\(\pm\) 0.2 & 4.4 \({}^{\text{a}}\)\(\pm\) 0.1 & 1.1 \(\pm\) 0.0 & 11.2 \({}^{\text{b}}\)\(\pm\) 0.2 \\ \hline \multicolumn{5}{c}{**Tocopherol**} \\ \cline{2-5}  & \multicolumn{2}{c}{**\(\alpha\)**} & \multicolumn{2}{c}{\(\beta\) + \(\gamma\)} & \(\Delta\) \\ \hline Eggs F & 77.8 \({}^{\text{a}}\)\(\pm\) 1.5 & 5.2 \({}^{\text{a}}\)\(\pm\) 0.1 & 0.8 \({}^{\text{a}}\)\(\pm\) 0.0 & 83.7 \({}^{\text{a}}\)\(\pm\) 1.7 \\ Eggs C & 89.9 \({}^{\text{b}}\)\(\pm\) 2.4 & 1.7 \({}^{\text{b}}\)\(\pm\) 0.0 & 0.3 \({}^{\text{b}}\)\(\pm\) 0.0 & 91.3 \({}^{\text{b}}\)\(\pm\) 2.5 \\ \hline \multicolumn{5}{c}{**not**: not detected; averages marked with different letters (a, b), within the column, are significantly different (\(p<0.05\), LSD test).} \\ \end{tabular}
\end{table} 
Table 2: The content of carotenoids [ug/g] and tocopherols [ug/g] in egg yolk from caged hens (C eggs) and free range hens (eggs F), n = 60. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multicolumn{3}{c}{**Yolk Color Parameters**} \\ \cline{2-4}  & **L* (C)** & **a* (C)** & **b* (C)** \\ \hline Eggs F & 51.61 \({}^{\text{a}}\)\(\pm\) 2.45 & 3.36 \({}^{\text{a}}\)\(\pm\) 0.15 & 45.69 \({}^{\text{a}}\)\(\pm\) 1.79 \\ Eggs C & 49.60 \({}^{\text{a}}\)\(\pm\) 2.27 & 2.93 \({}^{\text{b}}\)\(\pm\) 0.74 & 40.05 \({}^{\text{b}}\)\(\pm\) 1.33 \\ \hline \hline \end{tabular} \({\rm L}^{*}\)—psychometric brightness of color, a*—amount of red, b*—amount of yellow, averages marked with different letters (a, b), within the column, are significantly different (\(p<0.05\), LSD test).  
\end{table}