## 2 Materials and Methods
### Chemical Analyses  
At silo opening, the topmost moldy or spoiled part (about 100 g) of silages was discarded, with the remaining mass mixed thoroughly. Twenty grams of each fresh silage \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**NR**} & \multirow{2}{*}{**PD**} & \multicolumn{2}{c}{**Alfalfa FM Yield, t ha\({}^{-1}\)**} & \multicolumn{2}{c}{**Corn FM Yield, t ha\({}^{-1}\)**} & \multicolumn{2}{c}{**Alfalfa Proportion in Silage, \%**} \\ \cline{3-8}  & & **2017** & **2018** & **2017** & **2018** & **2017** & **2018** \\ \hline N0 \({}^{\text{a}}\) & D30 \({}^{\text{b}}\) & 5.26 Aa & 5.05 a & 29.66 Bb & 20.42 Bb & 18 Aa & 25 Aa \\  & D45 & 2.75 B & 3.40 & 33.59 ABb & 24.52 AB & 8 B & 14 B \\  & D60 & 1.54 B & 3.17 & 37.84 A & 27.83 Ab & 5 C & 11 B \\ N60 & D30 & 3.23 c & 2.67 b & 34.70 Bab & 26.61 ab & 9 b & 10 b \\  & D45 & 3.24 & 2.06 & 38.30 ABab & 31.61 & 8 & 8 \\  & D60 & 2.48 & 1.81 & 40.80 A & 32.81 ab & 6 & 6 \\ N120 & D30 & 3.41 Ac & 3.82 ab & 34.78 ab & 25.39 ab & 10 Ab & 15 b \\  & D45 & 3.18 A & 2.56 & 39.84 ab & 32.20 & 8 AB & 8 \\  & D60 & 2.73 B & 2.08 & 39.11 & 33.37 ab & 7 B & 7 \\ N180 & D30 & 4.38 Ab & 3.90 Aab & 36.36 Ba & 27.30 Ba & 12 b & 14 Ab \\  & D45 & 2.28 B & 2.43 AB & 45.37 Aa & 31.95 A & 5 & 8 AB \\  & D60 & 1.19 B & 1.17 B & 47.26 A & 36.07 Aa & 3 & 3 B \\  & Mean & 3.00 & 2.84 & 38.57 & 30.21 & 9 & 11 \\  & SEM \({}^{\text{c}}\) & 0.19 & 0.21 & 0.91 & 0.97 & 0.01 & 0.01 \\  & \multicolumn{6}{c}{Source of variation \(\rho\) value} \\ NR & ns \({}^{\text{d}}\) & ns & 0.022 & 0.013 & 0.020 & 0.010 \\ PD & \textless{}0.001 & \textless{}0.001 & \textless{}0.001 & \textless{}0.001 & \textless{}0.001 & \textless{}0.001 \\ NR \(\times\) PD & \textless{}0.001 & ns & ns & ns & \textless{}0.001 & ns \\ \hline \hline \end{tabular}  
* Different lowercase letters in the same column indicate significant differences at \(p\)\(<\) 0.05 among N application rates under the same corn plant density, and different capital letters in the same column indicate significant differences at \(p\)\(<\) 0.05 among corn plant densities under the same N rate. \({}^{\text{a}}\) N0, N60, N120 and N180 mean N application rate of 0, 60, 120 and 180 kg N ha\({}^{-1}\). \({}^{\text{b}}\) D30, D45 and D60 mean corn plant density of 30, 45 and 60 thousand plants ha\({}^{-1}\). \({}^{\text{c}}\) Standard error of the overall mean. \({}^{\text{d}}\) ns indicates not significant at \(p\)\(<\) 0.05.
* \end{table} 
Table 1: Forage fresh matter (FM) yield and alfalfa proportion (FM basis) in mixed silage of alfalfa–silage corn relay intercropping as affected by nitrogen application rate (NR) and corn plant density (PD). sample was homogenized in a blender with 180 mL of distilled water for 2 min, and then filtered through four layers of cheesecloth and one layer of qualitative filter paper. Afterward, pH value was measured immediately using an electrode pH meter (PHS-3C, INESA, Shanghai, China). Then the filtrate was centrifuged at 20,000 g for 10 min and reserved for fermentation acids and ammoniacal nitrogen (NH\({}_{3}\)-N) analyses. Lactic acid (LA), acetic acid (AA), propionic acid (PA) and butyric acid (BA) were determined by high performance liquid chromatography (HPLC) (LC-20A; Shimadzu, Tokyo, Japan). The analytical conditions were as follows: column, Shodex RSpak KC-811S-DVB gel C (8.0 mm \(\times\) 30 cm, Shimadzu); oven temperature, 50 \({}^{\circ}\)C; mobile phase, 3 mmol L\({}^{-1}\) HClO\({}_{4}\); flow rate, 1.0 mL min\({}^{-1}\); injection volume 5 \(\mu\)L; detector, SPD-M20 AVP (Shimadzu). The NH\({}_{3}\)-N concentration was determined by the phenol-hypochlorite colorimetric method according to Broderick and Kang [26]. V-score was calculated by the proportion of NH\({}_{3}\)-N in the total nitrogen and fermentation acid contents in the silage (percent of fresh weight) to assess the fermentation quality ([PERSON] et al., 2016).