Statement-1: When ${\mathrm{CO}}_2$ is passed through lime water, it first turns milky and then the solution becomes clear when the passage of ${\mathrm{CO}}_2$ is continued.

Statement-2: The milkiness is due to the formation of insoluble ${\mathrm{CaCO}}_3$ which then changes to soluble $\mathrm{Ca}{({\mathrm{HCO}}_3 )}_2$ when excess of ${\mathrm{CO}}_2$ is present

When carbon dioxide is carried through lime water, the solution first appears milky; however, as the carbon dioxide is continued to travel through, the solution turns clear. 
Because the development of insoluble calcium carbonate—which transforms into soluble Calcium Hydrogen Carbonate when there is an excess of carbon di oxide—causes the milky disappearance.