Maxwell enunciated the theorem that "If unit loads rest upon a beam at the two points R and S, the deflection at R due to the unit load at S equals the deflection at S due to the load at R."

Explanation:

1. Background:
To understand the theorem, it is important to have a basic understanding of beam deflection. When a load is applied to a beam, it causes the beam to deform or deflect. The deflection of a beam depends on various factors such as the load magnitude, beam material properties, beam geometry, and support conditions.

2. Theorem Statement:
The theorem states that if unit loads (load with magnitude equal to 1) are applied at two different points, R and S, on a beam, the deflection at point R due to the unit load at S will be equal to the deflection at point S due to the unit load at R.

3. Significance:
This theorem has significant implications in structural analysis and design. It allows engineers to simplify calculations by considering the deflection at one point due to a unit load at another point instead of analyzing the entire beam under the actual loads. This simplification is particularly useful in situations where complex loadings are involved.

4. Example:
To illustrate the theorem, let's consider a simply supported beam with a unit load applied at points R and S. According to the theorem, the deflection at point R due to the unit load at S will be equal to the deflection at point S due to the unit load at R.

5. Calculation:
To calculate the deflection at a specific point due to a unit load at another point, engineers use various methods such as the principle of virtual work or energy methods like the Castigliano's theorem. The theorem attributed to Maxwell is a specific case of these methods.

6. Conclusion:
In conclusion, Maxwell enunciated the theorem that states the deflection at one point on a beam due to a unit load at another point is equal to the deflection at the latter point due to the unit load at the former point. This theorem is widely used in structural analysis and design to simplify calculations and determine the deflections of beams.