This section of the book is from the "Household Companion: The Home Book Of Etiquette" book.
If a gentleman desires to offer his seat to a lady, he should not beckon to her, but rise and offer it to her courteously. It is the duty of the lady, in accepting the seat, to acknowledge his courteous attention by a bow and an audible expression of thanks. On the other hand it is an indication of ill-breeding to show signs of displeasure if, on entering a crowded car, no seat is offered. It should be borne in mind that the gentleman has a right to his seat, and is under no obligation, except that of politeness, to give it up, and weariness or weakness may render it inadvisable for him to rise. No lady, if young or strong, will expect or permit an old gentleman to relinquish to her his seat. If, however, a lady is ill or greatly fatigued she should not hesitate to request a seat, giving her reasons for doing so. No gentleman, and few who are not gentlemen, would refuse such a request.
No gentleman will take a vacant seat while ladies are standing, and none should stand on the car platform in such a manner as to discommode alighting passengers. It is easy and courteous to move aside, and step down into the street if necessary. If baskets or bundles are brought into the car care should be taken not to let them annoy passengers.