1. **Problem Statement:** Given a quadrilateral PQRS where points P, Q, R, S are such that PQ=QR=RS=PN, and QS is a line with point M on SR where PM=KMN and QM=KMS. We are given: i. $PMS = \frac{K_1}{(4+3a)b}$ ii. $PM = \frac{K_2}{(b+3a)b}$ iii. PN and PM are angles of refraction of high magnitude on an equipotential surface. We need to understand K1 and K2 constants in this context. 2. **Step 1 - Analyze given relations:** - $PMS$ and $PM$ are given in fractional form involving $K_1,K_2,a,b$. These appear to represent forces or displacements dependent on geometric parameters $a,b$. 3. **Step 2 - Understand K1 and K2:** - Since $PMS = \frac{K_1}{(4+3a)b}$ and $PM = \frac{K_2}{(b+3a)b}$, $K_1$ and $K_2$ are proportional constants likely related to material or force constants connected with these segments. 4. **Step 3 - Relationship between PN and PM:** - PN and PM represent angles or forces acting on the equipotential surface, whose magnitudes relate to $K_1$ and $K_2$ respectively. 5. **Step 4 - Problem (b):** - Forces $P, 2P, 3P, 4P$ act on an object with total force 5P, distributed over 4 bodies, with rest forces balancing. - The goal is to study the equilibrium of forces obeying the law of conservation of momentum and energy. 6. **Step 5 - For problem (15):** - Quadrilateral ABCD with sides AB, BC, CD defined with lengths involving parameters $2a$ and $2d$. - We are to determine: 1) If AB is a double-constructed minister (possibly meaning double length or double force). 2) Dynamism at joints A and C. 3) Whether BD is ministerial (structurally stable or force-related). 7. **Summary:** The problem mainly involves analyzing mechanical equilibria, forces, and geometric relations with given constants $K_1,K_2,a,b$ and forces proportional to P. **Final remarks:** - Constants $K_1,K_2$ represent proportionality constants for force or displacement measures. - Angles PN and PM are related to refraction angles on an equipotential surface. - The equilibrium of forces with magnitudes $P, 2P, 3P, 4P$ respect balance and conservation laws. - Structural stability and forces in the quadrilateral ABCD with lengths $2a$ and $2d$ need to be verified by computations. **No explicit numeric values or further equations provided to solve quantitatively.**