"Vicarious liability" means legal responsibility for a tort committed by another person or entity. It is a legal doctrine that says, in plain language, "the buck stops here." As stated in California Civil Code sec. 2338:

Unless required by or under the authority of law to employ that particular agent, a principal is responsible to third persons for the negligence of his agent in the transaction of the business of the agency, including wrongful acts committed by such agent in and as a part of the transaction of such business, and for his willful omission to fulfill the obligations of the principal.

In Baker v. Kinsey (1869) 38 Cal. 631 the court held that an action to recover damages for the bite of a vicious dog belonging to the toll-keeper cannot be maintained against the owner of the bridge if it appears that the owner of the bridge did not keep or harbor the dog in person, and did not authorize or require the tollkeeper to keep the dog, and did not know that the dog was being used in the conduct or protection of the business in which the owner of the dog was employed. 

Here are some examples based on California cases in a variety of situations not involving dog bites:

In Walsh v. Hunt (1898) 120 Cal. 46, the supreme court was considering the act of an agent to whom an executed note and mortgage had been left for delivery. The agent altered the figures evidencing the principal sum and the rate of interest. The court held that the agent was a mere bailee for delivery. The supreme court mentions this case in Otis Elevator Co. v. First Nat. Bank, supra, and says that "it is not at all in point in this matter."

In Rahmel v. Lehndorff (1904) 142 Cal. 681 it was held that an innkeeper was not liable for an assault and battery committed by a waiter in a dining room upon one of his guests. This case is distinguished in Ruppe v. City of Los Angeles (1921) 186 Cal. 400, where the supreme court says: "Something, perhaps, should also be said as to the statement in the second sentence quoted from Rahmel v. Lehndorff, that 'the wrongful act must be one which the servant is empowered under some circumstances to do.' If this be taken to mean that the act must be one which the servant is authorized in some circumstances to do, the statement is undoubtedly too narrow." A simple illustration is given, and the court goes on to say: "In other words, while the master has not empowered the servant to break the law in the sense that he has authorized him to do so, he has empowered him in the sense that he has entrusted him with the performance of a duty in whose performance it is possible for him to break the law."

In Riordan v. Gas Consumers' Association (1906) 4 Cal.App. 639, 643: "The question generally is whether the servant at the very time of the alleged act of negligence, had departed from his employment, or whether he departed from or neglected a duty in the line of his employment. In the first case, the principal is not responsible for the servant's acts, and in the second case he is responsible."

Hopkins v. Western Pacific Railroad Co. (1875) 50 Cal. 190 was an action for damages for the construction of a railroad. In the syllabus to the decision appears this statement: "A railroad company is not responsible for the acts of its employee in creating a nuisance by using a culvert under its railroad near the residence of plaintiff for the purpose of a privy." 

Stephenson v. Southern Pacific Co. (1892) 93 Cal. 558 was a case where an engineer backed his engine toward a street car crossing the railroad track with the simple intent to frighten passengers on the street car. A frightened passenger, believing herself in danger, jumped from the street car and was injured. Held, that the act of the engineer was not done in the scope of his employment.

In Copelin v. Berlin Dye Works Etc. Co. (1914) 168 Cal. 715, jewelry was left in a suit of clothes delivered to the driver of one of the defendant's wagons for the purpose of having the clothes cleaned. The jewelry disappeared. It was held that the cleaning company was not chargeable as an involuntary or gratuitous bailee so as to be liable for the theft of the jewelry. The court pointed out that the cleaning company assumed no duty of safekeeping the jewelry and delegated no such duty to its servants, and hence the court held that the theft was not within the scope of the employment.