A series of tests are conducted in which a simply-supported beam is loaded with a range of weights. The beam length is $20 cm$ and it has a square cross-section of $8 mm$ width. The beam is steel. Weights of $10 N$, $15 N$, $20 N$, $25 N$, and $30 N$ are applied to the middle of the beam and deflections of $0.155 mm$, $0.232 mm$, $0.309 mm$, $0.386 mm$, and $0.464 mm$ are recorded. Determine an approximate value of the constant $a$ in the deflection formula $C P^a L^b/(EI)$).

A. $a = 0$
B. $a = 0.5$
C. $a = 1$
D. $a = 2$
E. $a = 3$