Introduction:
The epidermis is the outermost layer of cells in plants and animals. It serves as a protective barrier and performs various functions to ensure the well-being and survival of the organism. In the given options, gaseous exchange, protection from adverse conditions, and transpiration are all functions of the epidermis. However, conduction of water is not a primary function of the epidermis.

Explanation:
The epidermis is primarily responsible for protecting the underlying tissues and organs from external factors and adverse conditions. It acts as a barrier against physical damage, pathogens, and excessive water loss. Let's discuss each of the given options in detail:

1. Protection from adverse conditions:
The epidermis forms a protective layer that shields the underlying tissues from harmful environmental factors such as UV radiation, extreme temperatures, and mechanical injuries. It prevents the entry of pathogens and minimizes water loss, thereby maintaining the internal environment of the organism.

2. Gaseous exchange:
Plants have specialized openings called stomata on their epidermis, which allow for the exchange of gases such as oxygen and carbon dioxide. These stomata open and close to regulate the intake of carbon dioxide for photosynthesis and the release of oxygen and excess water vapor through transpiration.

3. Conduction of water:
While the epidermis plays a role in the overall transport of water in plants, it is not primarily responsible for the conduction of water. This function is mainly carried out by the xylem, a specialized tissue that transports water and dissolved minerals from the roots to the rest of the plant. The epidermis helps in preventing excessive water loss through its cuticle and regulating water uptake through the roots, but it does not conduct water throughout the plant.

4. Transpiration:
Transpiration is the process by which plants lose water vapor through the stomata in their epidermis. It helps in maintaining the water balance, cooling the plant, and facilitating the upward movement of water and nutrients from the roots. The epidermis, along with the stomata, plays a crucial role in regulating transpiration.

Therefore, the correct answer is option 'C' - Conduction of water is not a function of the epidermis.