"The police" during this period were considered a peace keeping force. They developed out of either voluntary militia in rural communities, dedicating to protecting life and property, or out of military rule to both protect and subdue citizens. Therefore, the police at the time were not connected to the idea of "solving" crimes, but more to the arrest and punishment of criminals.
The detective is a variation on this because he seeks out to solve the crime, how it happened and not just who committed it. The detective represents intellectual prowess, which wins out over physical strength. The character better represents the police of today than the police of the 19th century, and the detective could be thought of as forerunner to the characters of CSI.
In Auguste Dupin, Edgar Allan Poe introduced a new type of detective, the amateur detective, and established some of the conventions which Arthur Conan Doyle copied with his Sherlock Holmes. Some essential conventions of the amateur detective tale are encapsulated in a few lines of dialogue in Poe's "The Murders in the Rue Morgue."
As for these murders, let us enter into some examinations for ourselves, before we make up an opinion respecting them. An inquiry will afford us amusement. [I thought this an odd term, so applied, but said nothing] And, besides, Le Bon once rendered me a service for which I am not ungrateful. We will go and see the premises with our own eyes. I know G____, the Prefect of Police, and shall have no difficulty in obtaining the necessary permission."
The amateur detective frequently becomes involved with criminal investigations out of curiosity or boredom. Since he has no official status, he needs the consent and assistance of a police official in order to get involved with crimes such as murder. This police official serves as an aegis. Dupin is on good terms with Monsieur G-, who is the highest ranking officer in the Parisian police force. (With Holmes it is usually Inspector Lestrade or some other police inspector.) Because of his relationship with G-, Dupin is able to visit the scene of the crime (and to take the reader along with him to the grisly scene).
Le Bon is an innocent man suspected of committing the murders for money. Because Dupin feels grateful to him, he has an emotional motive for wanting to solve the crime and vindicate Le Bon. It is desirable that an amateur detective should have a stronger motive than curiosity or even financial reward because it makes his character more sympathetic to the reader. This kind of emotional motive is frequently seen in Doyle's stories and novels about Sherlock Holmes, and it is frequently found in modern private detective stories, such as Raymond Chandler's The Big Sleep and Dashiell Hammett's The Maltese Falcon.
Like Dupin, Sherlock Holmes has superior intellectual powers and feels a need to use them in order to stave off boredom. Both Dupin and Sherlock Holmes are "armchair detectives." Like their readers, they like to lounge in comfortable chairs smoking their pipes and indulging in reverie. Their ability to solve problems brings them rewards which enable them to lead lives of independence and leisure which their readers would love to be able to emulate. Dupin gets a reward of fifty thousand francs, a small fortune, in "The Purloined Letter."