# Determination of Seed Volume Based on Selected Seed Dimensions
## 3 Results and Discussion
### Coefficients of Seed Volume  
The seed volume coefficients for the analyzed plant species are presented in Table 3. The value of this parameter, calculated with Equation (6), ranged from 0.376 (_Pseudotsuga menziesii_) to 0.537 (_Tilia cordata_). A typically ellipsoidal seed has a volume coefficient of \(\pi/6=0.524\)[8]. The calculated volume coefficients indicate that _Cornu s macrophylla_, _Pica abies_, and _Cornu sanguinea_ have ellipsoidal seeds; therefore, the ellipsoid can be used as a model figure to determine the volume of seeds in these plant species. In this case, the error in seed volume calculations (the percentage of the product of the absolute difference between coefficient \(k_{0}\) and the volume coefficient of an ellipsoid relative to the volume coefficient of an ellipsoid) reached 0.27%, 0.31%, and 0.65%, respectively. The volume coefficient of _Pseudotsuga menziesii_ seeds was least similar to that of an ellipsoid, and the error in seed volume calculations was very high at 39.25%. In the analyzed species, the remaining seed volume coefficients were determined within the following range of values:  
* \(k_{1}\)--from 0.098 to 0.468,
* \(k_{2}\)--from 0.188 to 0.502,
* \(k_{3}\)--from 0.195 to 0.488,  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Seed Species** & \(L\) **(mm)** & \(W\) **(mm)** & \(T\) **(mm)** & \(D\) **(mm)** & \(R\) **(-)** & _\(\Phi\) **(-)** & \(V\) **(mm\({}^{3}\))** \\ \hline _Pseudotsuga menziesii_ & 6.93 \({}^{\text{a}}\) & 3.48 \({}^{\text{d}}\) & 1.83 \({}^{\text{f}}\) & 3.53 \({}^{\text{c}}\) & 0.504 \({}^{\text{h}}\) & 0.510 \({}^{\text{i}}\) & 16.71 \({}^{\text{d}}\) \\ _Pica abies_ & 4.21 \({}^{\text{de}}\) & 2.22 \({}^{\text{g}}\) & 1.52 \({}^{\text{g}}\) & 2.41 \({}^{\text{h}}\) & 0.531 \({}^{\text{g}}\) & 0.576 \({}^{\text{h}}\) & 7.49 \({}^{\text{f}}\) \\ _Juniperus communis_ & 4.08 \({}^{\text{e}}\) & 2.24 \({}^{\text{g}}\) & 1.81 \({}^{\text{f}}\) & 2.54 \({}^{\text{g}}\) & 0.552 \({}^{\text{f}}\) & 0.625 \({}^{\text{g}}\) & 7.31 \({}^{\text{f}}\) \\ _Cotoneaster horizontalis_ & 4.36 \({}^{\text{d}}\) & 3.38 \({}^{\text{e}}\) & 1.78 \({}^{\text{f}}\) & 2.96 \({}^{\text{f}}\) & 0.782 \({}^{\text{e}}\) & 0.683 \({}^{\text{f}}\) & 11.78 \({}^{\text{e}}\) \\ _Frangula minus_ & 4.70 \({}^{\text{e}}\) & 4.00 \({}^{\text{c}}\) & 2.20 \({}^{\text{e}}\) & 3.45 \({}^{\text{d}}\) & 0.853 \({}^{\text{c}}\) & 0.736 \({}^{\text{e}}\) & 20.99 \({}^{\text{c}}\) \\ _Juniperus scopulorum_ & 4.10 \({}^{\text{e}}\) & 3.22 \({}^{\text{f}}\) & 2.55 \({}^{\text{d}}\) & 3.22 \({}^{\text{e}}\) & 0.789 \({}^{\text{e}}\) & 0.787 \({}^{\text{d}}\) & 15.74 \({}^{\text{d}}\) \\ _Tilia cordata_ & 3.83 \({}^{\text{f}}\) & 3.17 \({}^{\text{f}}\) & 2.74 \({}^{\text{c}}\) & 3.21 \({}^{\text{e}}\) & 0.832 \({}^{\text{d}}\) & 0.842 \({}^{\text{e}}\) & 18.22 \({}^{\text{d}}\) \\ _Cornu sanguinea_ & 5.15 \({}^{\text{b}}\) & 4.68 \({}^{\text{a}}\) & 4.26 \({}^{\text{a}}\) & 4.68 \({}^{\text{a}}\) & 0.909 \({}^{\text{b}}\) & 0.909 \({}^{\text{b}}\) & 54.87 \({}^{\text{a}}\) \\ _Cornu s macrophylla_ & 4.34 \({}^{\text{d}}\) & 4.16 \({}^{\text{b}}\) & 3.89 \({}^{\text{b}}\) & 4.13 \({}^{\text{b}}\) & 0.960 \({}^{\text{a}}\) & 0.951 \({}^{\text{a}}\) & 37.92 \({}^{\text{b}}\) \\ \hline \hline \end{tabular} \({}^{\text{L}}\)—length, _W_—width, _T_—thickness, _D_—geometric mean diameter, _R_—spect ratio, _\(\Phi\)_—sphericity index, _V_—volume; and \({}^{\text{a}}\cdots\)—superscript letters denote significant differences between properties at \(p\) < 0.05 (Tukey’s test).  
\end{table}
Table 2: Mean values of the physical properties of seeds and the significance of differences.  
Equation (17) produced the highest values, and Equation (15) produced the lowest values of the coefficient of seed volume, which can be directly attributed to the dimensions applied in the calculations (smallest and largest, respectively).