# Determination of Seed Volume Based on Selected Seed Dimensions
## 3 Results and Discussion
### Error in Seed Volume Calculations  
In the calculations of individual seed volume, the smallest potential error was generated by Equation (18), which is based on all three basic dimensions. For this reason, seed volume calculated with Equation (18) was regarded as the baseline value when determining errors in volume calculations based on two or one basic seed dimensions. Obviously, when the sample is large enough, total seed volume is similar regardless of the applied equation. However, the calculated volumes of individual seeds differ from the baseline value (they can be higher or lower than the baseline value), which can lead to certain errors. The mean error values in volume calculations involving simplified equations (based on two or one basic dimensions) are presented in Figure 2. Depending on the applied equation, the errors in seed volume calculations fall within the following ranges:  
* _Pseudotsuga menziesii_--from 7.3% to 16.9%,
* _Picea abies_--from 9.3% to 19.3%,
* _Juniperus communis_--from 7.7% to 25.9%,
* _Cotonester horizontalis_--from 10.2% to 19.1%,
* _Frangula alnus_ Mill.--from 7.1% to 14.5%,
* _Juniperus scopulorum_--from 8.6% to 21.2%,
* _Tilia cordata_--from 6.9% to 15.6%,
* _Cornus sanguinea_--from 3.7% to 10.8%,
* _Cornus macrophyllla_--from 2.7% to 8.0%. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{**Seed**}} & \multicolumn{8}{c}{**Coefficient of Seed Volume Calculated as:**} \\ \cline{2-11}
**Species** & \(L\cdot W\cdot T\) & \(L^{2}\cdot W\) & \(L^{2}\cdot T\) & \(W^{2}\cdot L\) & \(W^{2}\cdot T\) & \(T^{2}\cdot L\) & \(T^{2}\cdot W\) & \(L^{3}\) & \(W^{3}\) & \(T^{3}\) \\ \hline _Pseudotsuga menziesii_ & 0.376 & 0.098 & 0.188 & 0.195 & 0.745 & 0.714 & 1.421 & 0.049 & 0.386 & 2.674 \\ _Pica abies_ & 0.522 & 0.187 & 0.274 & 0.352 & 0.978 & 0.761 & 1.440 & 0.097 & 0.653 & 2.085 \\ _Juniperus communis_ & 0.431 & 0.192 & 0.236 & 0.344 & 0.767 & 0.528 & 0.958 & 0.104 & 0.599 & 1.171 \\ _Cotonester horizontalis_ & 0.466 & 0.182 & 0.345 & 0.233 & 0.567 & 0.837 & 1.073 & 0.140 & 0.294 & 1.995 \\ _Frangula alnus_ & 0.505 & 0.235 & 0.429 & 0.275 & 0.590 & 0.917 & 1.076 & 0.199 & 0.320 & 1.942 \\ _Juniperus scopulorum_ & 0.459 & 0.286 & 0.362 & 0.362 & 0.573 & 0.575 & 0.722 & 0.223 & 0.451 & 0.898 \\ _Tilia cordata_ & 0.537 & 0.381 & 0.442 & 0.462 & 0.646 & 0.619 & 0.747 & 0.312 & 0.554 & 0.858 \\ _Cornus sanguinea_ & 0.527 & 0.437 & 0.479 & 0.480 & 0.577 & 0.578 & 0.633 & 0.396 & 0.525 & 0.693 \\ _Cornus macrophyllla_ & 0.525 & 0.468 & 0.502 & 0.488 & 0.548 & 0.562 & 0.587 & 0.447 & 0.509 & 0.628 \\ \hline \hline \end{tabular} \(L\)–length, \(W\)—width, and \(T\)—thickness.  
\end{table} 
Table 3: Coefficients of seed volume. When seed volume was calculated based on two basic dimensions, the smallest error (2.7%) was noted in _Cornus macrophylla_ (d2--formula based on the product of the square of seed length and seed thickness), and the greatest error (14.3%) was noted in _Juniperus communis_ (d4--formula based on the product of the square of seed width and seed thickness). Therefore, volume should be calculated with the use of Formula (17) for _Pica abies_ and _Juniperus communis_ seeds, Formula (18) for _Frangula almus_ and _Cornus macrophylla_ seeds, formula 19 for _Cotomaster horizontalis_ seeds, and Formula (21) for _Juniperus scopulorum_, _Tilia cordata_ and _Cornus samguinea_ seeds. The mean error in seed volume calculations based on two basic dimensions was similar regardless of the applied formula, and the smallest error (8.2%) was noted for the equation based on the product of the square of seed thickness and seed length, whereas the greatest error (8.5%) was noted for the equation based on the product of the square of seed length and seed thickness. Somewhat smaller errors was observed when the volume of an individual seed was determined using equations based on the square of the smaller dimension (Formulas (21), (23), and (24)).