(a) That's right. Authority to act on behalf of another person may arise by law as a result of necessity in situations of emergency. This is termed 'agency of necessity'. When agency of necessity arises, the agent is entitled to be reimbursed by the principal for reasonable expenses incurred. The principal is also bound to third parties who have dealt with the agent of necessity. Agency of necessity only arises if all of the following requirements are met.
1. The principal and agent have some recognised relationship such as shipowner and the owner of cargo; other carriers of goods, and bailees generally. The courts do not recognise that agency of necessity can arise between complete strangers.
2. It must be shown that in the circumstances, an emergency has arisen in which the principal will suffer harm unless action is taken. The harm may consist of a loss of property, damage to property, or economic harm.
3. It must be shown that the principal is absent so that they cannot act for themselves, and that, practically speaking, it is not possible to contact the principal for instructions.
4. The agent acts for the benefit and in the best interests of the principal, rather than for any self-interest.
In this example, all these requirements appear to be met. This means that A is legally bound to pay D for the costs of looking after and feeding the horse.