In England, a lady may accept the arm of a gentleman with whom she is walking, even though he be only an acquaintance. This is not the case either in America or on the Continent. There a lady can take the arm of no gentleman who is not either her husband, lover, or near relative.
If a lady has been making purchases during her walk, she may permit the gentleman who accompanies her to carry any small, parcel that she may have in her own hand; but she should not burthen with more than one under any circumstances whatever.
Two ladies may without impropriety take each one arm of a single cavalier; but one lady cannot, with either grace or the sanction of custom take the arms of two gentlemen at the same time.
When a lady is walking with a gentleman in a park, or public garden, or through the rooms of an exhibition, and becomes fatigued, it is the gentleman's duty to find her a seat. If, however, as is very frequently the case, he is himself obliged to remain standing, the lady should make a point of rising as soon as she is sufficiently rested, and not abuse either the patience or politeness of her companion.
It is the place of the lady to bow first, if she meets a gentleman of her acquaintance. When you meet friends or acquaintances in the streets, the exhibitions, or any public places, be careful not to pronounce their names so loudly as to attract the attention of bystanders. Never call across the street, or attempt to carry on a dialogue in a public vehicle, unless your interlocutor occupies the seat beside your own.
Source: Routledge, George. The Well-Bred Person's Book of Etiquette. (Gloucestershire: The History Press, 1891), 27-28.