The head loss through the bed of solids in a filter can be determined using the combination of the Carmen-Kozney equation and the Rose equation. This combination provides a more accurate estimation of the head loss compared to using either equation alone.

1. Carmen-Kozney Equation:
The Carmen-Kozney equation is commonly used to estimate the pressure drop or head loss in porous media, such as a bed of solids in a filter. It is based on the assumption that the flow through the porous media is laminar and follows Darcy's law. The equation is given by:

ΔP/μ = (150 (1 - ε)^2 L^2)/(ε^3 d^2) + (1.75 (1 - ε) L)/(ε^3 d) + (1.75 L)/(ε^2 d)

Where:
ΔP = Pressure drop across the bed of solids
μ = Viscosity of the fluid
ε = Porosity of the bed of solids
L = Length of the bed
d = Equivalent diameter of the solids

2. Rose Equation:
The Rose equation is another commonly used equation to estimate the head loss through a bed of solids. It takes into account the effects of particle size distribution and shape on the pressure drop. The equation is given by:

ΔP/μ = (150 (1 - ε)^2 L^2)/(ε^3 d^2) + (1.75 (1 - ε) L)/(ε^3 d) + (1.75 L)/(ε^2 d) + K (1 - ε)^2 (1 - εmin)^2

Where:
ΔP = Pressure drop across the bed of solids
μ = Viscosity of the fluid
ε = Porosity of the bed of solids
L = Length of the bed
d = Equivalent diameter of the solids
K = Constant related to the shape of the particles
εmin = Minimum porosity of the bed

3. Combination of Carmen-Kozney and Rose Equations:
The combination of the Carmen-Kozney and Rose equations provides a more accurate estimation of the head loss through the bed of solids in a filter. The Carmen-Kozney equation accounts for the flow through the porous media, while the Rose equation takes into consideration the effects of particle size distribution and shape. By using both equations together, the estimation of head loss is improved.

Therefore, the correct answer is option 'C' - Carmen-Kozney and Rose equation.