A GENTLEMAN OFFERS HIS ARM
To an old lady or to an invalid a gentleman offers his arm if either of them wants his support. Otherwise a lady no longer leans upon a gentleman in the daytime, unless to cross a very crowded thoroughfare, or to be helped over a rough piece of road, or under other impeding circumstances. In accompanying a lady anywhere at night, whether down the steps of a house, or from one building to another, or when walking a distance, a gentleman always offers his arm. The reason is that in her thin high-heeled slippers, and when it is too dark to see her foothold clearly, she is likely to trip.
Under any of these circumstances when he proffers his assistance, he might say: “Don’t you think you had better take my arm? You might trip.” Or—“Wouldn’t it be easier if you took my arm along here? The going is pretty bad.” Otherwise the only occasions on which a gentleman offers his arm to a lady are in taking her in at a formal dinner, or taking her in to supper at a ball, or when he is an usher at a wedding. Even in walking across a ballroom, except at a public ball in the grand march, it is the present fashion for the younger generation to walk side by side, never arm in arm. This, however, is merely an instance where etiquette and the custom of the moment differ. Old-fashioned gentlemen still offer their arm, and it is, and long will be, in accordance with etiquette to do so. But etiquette does not permit a gentleman to take a lady’s arm!
From Etiquette, by Emily Post