Final answer:
The ratio of the heights to which water and mercury are raised by capillary action in the same glass tube is determined by the adhesion and cohesion properties of the liquids. Water rises higher than mercury due to stronger adhesion forces relative to cohesion in water, whereas mercury exhibits strong cohesion and does not rise as much.
Step-by-step explanation:
To calculate the ratio of the heights to which water and mercury are raised by capillary action in the same glass tube, we need to understand the principles governing capillary action. Capillary action occurs due to the adhesion between the liquid molecules and the walls of the tube, as well as the cohesion among the liquid molecules themselves. When comparing water and mercury in the same tube, water exhibits strong adhesion and rises in the tube, while mercury, which has stronger cohesive forces, depresses.
Without detailed figures for the specific context of your tube and liquids, a direct numerical ratio cannot be provided. However, the concept allows us to understand that the height of water rise will be considerably higher than that of mercury due to water's higher adhesion relative to its cohesion, compared to mercury, which has higher cohesion. The jurisprudence of Spencer v. Hemmerde, which is unrelated to physics, does not apply here.