Cb is the block co-efficient or co-efficient of fitness is the ratio of the volume of displacement to the product of length, breadth and draught

$$\because\space C_{b}\space=\space{{\nabla}\over L\times B\times D}\:---\:1$$

$$C_{p}\space=\space{{\nabla}\over L\times A_{m}}\:---\:2$$

$$C_m \space = \space {{A_m} \over B \times D}$$

$$A_{m}=\:C_{m}\times B\times D\:---\:3$$

Substitute 3 in 2

$$C_{p}\space=\space{{\nabla}\over C_{m}\times B\times D\ \times L}\:---\:4$$

$$\nabla=C_{b}\times L\times B\times D\:---5\:\left(from\:equation\:1\right)$$

Substitute 5 in 4

$$C_{p}=\frac{C_{b}\times L\times B\times D}{C_{m}\times L\times B\times D}$$

$$C_p \space = \space {{C_b} \over C_m}$$