**Square system of planting:**

It is a widely adopted method of planting and is easy to perform. In this system, the plot is divided into squares, and trees are planted at the four corners of the square. Thus the distance between row to row and plant to plant becomes the same.

**Advantages:**

- Most easy and used widely.
- Facilitates cultural operations in two directions.
- Best supervision of the orchard is possible.
- A maintained irrigation system; straight irrigation channel to each plant.
- Spraying, harvesting, and intercultural operations can be done conveniently and easily.
- Quick-growing fruit trees like papaya, guava, banana can be planted during the early period of orchard establishment.

**Disadvantages:**

- Less number of trees are accommodated in the given area as compared to the hexagonal or quincunx system of planting.
- A certain amount of space in the center of the square is wasted.

**Rectangular system of planting:**

This method is similar to the square system. But the plot is divided into rectangles instead of squares, and trees are planted at the four corners of the rectangle in straight rows running at right angles. The only difference is that in this system more plants can be accommodated in the row keeping more space between the rows.

**Advantages:**

- This also facilitates cultural operations in two directions.
- Plants get proper space and sunlight for their development.
- Spraying, harvesting, and intercultural operations can be done conveniently and easily.
- Quick-growing vegetables and fruits can be planted in between two plants.

**Disadvantages:**

- A large area of the orchard is wasted if intercropping is not practiced.
- Less number of trees are accommodated in the given area as compared to the hexagonal or quincunx system of planting.
- Inter/filler crops can interfere with the growth of the main crop if not managed.

**Hexagonal system of planting:**

In this system, the trees are planted at the corners of an equilateral triangle, and thus six trees form a hexagon with the seventh tree at the center. It is generally followed where the land is very costly and fertile. It accommodates 15% more plants than the square system. This system provides equal space but it is difficult to layout.

**Advantages:**

- Accommodates 15% more plants than the square system.
- Cultivation of land between the tree rows is possible in three directions.
- Plants occupy the land fully without any waste as in the square systems.

**Disadvantages:**

- Intercultural operations become difficult.
- The layout is difficult and cumbersome and skill is required to layout the orchard.

**Quincunx system of planting:**

This system is exactly like the square system but one additional plant is planted in the center of each square. The plants that are planted in the center of each square are filler plants, eg: guava, papaya, peach, plum, etc. These filler plants are planted to generate additional income when the main orchard plant is under the non-bearing stage. The filler plants are uprooted when the main orchard trees start commercial fruiting.

**Advantages:**

- The number of plants planted by this system is almost double that of the square system.
- Additional income is earned from the filler crops.

**Disadvantages:**

- Interculture operations become difficult.
- Skill is required to layout the orchard.
- The spacing of the main crop is reduced if the filler crop is allowed to continue after the growth of the main crop.

**Contour system of planting:**

This system is generally followed in the hills with high slopes. First, the contour line is established. The contour line is an imaginary line that connects equal height on a slope. The contour line is so designed and graded in such a way that the flow of water in the irrigation channel becomes slow and thus finds time to penetrate the soil without causing erosion.

The trees are planted from base to top on the bench terrace prepared on the contour. One row of grasses is planted between the two rows of the main plant to reduce the flow of water.

**Advantages:**

- The best system of planting in hills that helps in controlling soil erosion.
- Preserves plant nutrients supplied by manures and fertilizers.
- It has good control of irrigation water and also reduces the velocity of the water.
- Interculture operations become easy to perform.

**Disadvantages:**

- Laying out of the contour is difficult and time-consuming.
- The number of plants per unit area will generally be less than other systems.
- Special skills are required to layout the system.

**Question:**

**Prove mathematically that the hexagonal system accommodates 16% more plants than the square system.**

**In square system:**

No. of plants = (Area in meter^{2}) / (planting distance)

Suppose, the total area is 10,000 sq. meters (1 ha) and the planting distance (plant to plant * row to row) is 10*10 meters. Then,

No. of plants = 10,000 / (10*10)

= 100

2. **In hexagonal system:**

No. of plants = (Area in meter2) / planting distance (plant * row spacing)

Suppose, plant to plant distance is 10 meters. Then row to row distance can be calculated as:

Let ABC be an equilateral triangle.

So,AC = BC = AB = 10 meter

A perpendicular line AD is drawn on BC which divides BC into two halves.

Thus, BD = DC = 5 meter

Now, In ∆ ADC

Using Pythagoras theorem,

AC^{2} = AD^{2} + DC^{2}

or, AD^{2} = AC^{2} – DC^{2}

or, AD^{2} = 10^{2} – 5^{2}

or, AD^{2} = 100 – 25

or, AD^{2} = 75

.’. AD = 8.66

So row to row distance will be 8.66 meter.

Now,

No. of plants = (Area in meter2) / planting distance (plant * row spacing)

= 10,000 / (10*8.66)

= 115.5

Hence it is proved that the hexagonal system accommodates 16% more plants than the square systems.

3. **In Quincunx system:**

Total No. of plants = plants planted in square system + Additionally planted plants in the center of the square

No. of plants in square system = (Area in meter2) / planting distance (plant * row spacing)

= 10,000 / (10*10)

= 100

Additionally planted plants in the center of the square = ( No. of rows lengthwise – 1) * (No. of rows widthwise – 1)

In 100 * 100 sq. meter field, if planting distance is 10 * 10 meters, then no. of rows lengthwise and widthwise will be 10 and 10.

So, No. of plants = (10 – 1) * (10 – 1)

= 9 * 9

= 81

Total No. of plants = plants planted in square system + Additionally planted plants in the center of the square

= 100 + 81

= 181

Hence, In the Quincunx system of planting, almost 2 times plants are accommodated in comparison to the square systems of planting.