I have a couple of old etiquette books. Fortunately, one of them, from 1913, is a free read on Google Books so I don't have to type.
It is obligatory to call on one's hostess after a dinner, a breakfast, a musicale, or a luncheon. But for men as well as women the dinner call is of paramount importance. It is paid within a fortnight after the dinner, and whether the invitation was accepted or not. When a dinner or dance invitation is declined, and no call is made afterward, a hostess has every reason to feel deeply offended and to accept the slight as a sign that her friendship and hospitality are not desired. Only very ignorant or ill bred persons pursue such a course with a view to dropping an undesirable acquaintance. If one wishes to drop an acquaintance, one should carefully pay the required call, and then let the interchange of visits cease.
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>Did gentlemen need chaperones? I thought they were for unmarried women?
When a single gentleman entertained, whether in his own home or at a theater or restaurant,
> [No matter how large or small the party is] if the guests are of both sexes, a married chaperon is necessary. She must be the first person invited and she should be asked by note or a personal call at her house.
For a dinner party:
>If there are women among his guests, he selects a married woman as the chaperon of the occasion. He is not at liberty to invite her however, without her husband, and it is considered in best taste to call upon the lady and make the request for her presence in person.
And, of course:
>A bachelor would not gather a party of men and women on board his yacht for a few hours sailing, or a dinner to view a race ,or enjoy a cruise without having someone to act as chaperon.
Inviting the chaperone makes it easier for the young ladies to attend:
>Young ladies attending a bachelor's tea or dinner are not required to go attended by their individual chaperons, the presence of a chaperon for the company at large, who stands in the place of a hostess, making that unnecessary. If at a bachelor's tea or dinner the chaperon rises early to leave, the other women must leave at the same time.
Since the young ladies are required to pay a party call afterwards, and since they cannot call upon a single gentleman, they pay the call to the chaperone instead.