According to Alexander von Humboldt:

Options

A. species richness decreases with increasing area of exploration
B. species richness increases with increasing area,but only up to limit
C. there is no relationship between species richness and area explored
D. species richness goes on increasing with increasing area of exploration

Answer

### Step-by-Step Solution

1. **Understanding the Species-Area Relationship**:
- Alexander von Humboldt proposed a relationship between the number of species (species richness) and the area being studied. This is known as the species-area relationship.

2. **Key Concept**:
- According to Humboldt, as the area increases, the species richness also increases, but this increase occurs only up to a certain limit.

3. **The Equation**:
- Humboldt formulated the equation for the species-area relationship:
\[ S = CA^Z \]
- Where:
- \( S \) = species richness
- \( A \) = area
- \( C \) = a constant (y-intercept)
- \( Z \) = regression coefficient (slope of the graph)

4. **Logarithmic Representation**:
- This equation can also be expressed in logarithmic form:
\[ \log S = \log C + Z \log A \]
- This form helps in visualizing the relationship on a graph.

5. **Analyzing the Options**:
- **Option A**: "Species richness decreases with increasing area of exploration."
- This is incorrect as Humboldt stated that species richness increases with area.
- **Option B**: "Species richness increases with increasing area but only up to a limit."
- This is correct and aligns with Humboldt's findings.
- **Option C**: "There is no relationship between species-area relationship and the area explored."
- This is incorrect since Humboldt established a clear relationship.
- **Option D**: "Species richness goes on increasing with increasing the exploring area."
- This statement is misleading as it does not mention the limit, making it incorrect.

6. **Conclusion**:
- The correct answer is **Option B**: "Species richness increases with increasing area but only up to a limit."