This section is from the book "Hill's Manual Of Social And Business Forms: A Guide To Correct Writing", by Thos. E. Hill. Also available from Amazon: Hill's Manual Of Social And Business Forms: The How-To-Do-Everything Book Of Victorian America.
ACCOMPANYING the salutation of hand-shaking, it is common, according to the customs of English-speaking people, to inquire concerning the health, news, etc. Offer the whole hand. It is an insult, and indicates snobbery, to present two fingers (Fig. 1) when shaking hands. It is also insulting to return a warm, cordial greeting with a lifeless hand ( Fig. 2), and evident indifference of manner, when hand-shaking. Present a cordial grasp (Fig. 3) and clasp the hand firmly, shaking it warmly for a period of two or three seconds, and then relinquishing the grasp entirely. It is rude to grasp the hand very tightly or to shake it over-vigorously. To hold it a very long time is often very embarrassing, and is a breach of etiquette. It is always the lady's privilege to extend the hand first. In her own house a lady should give her hand to every guest.
If both parties wear gloves, it is not necessary that each remove them in shaking hands; if one, however, has ungloved hands, it is courtesy for the other to remove the glove, unless in so doing it would cause an awkward pause; in which case apologize for not removing it, by saying, "Excuse my glove." The words and forms will always very much depend upon circumstances, of which individuals can themselves best judge. Kid and other thin gloves are not expected to be removed in hand-shaking; hence, apology is only necessary for the non- removal of the thick, heavy glove. As a rule in all salutations, it is well not to exhibit too much haste. The cool, deliberate person is the most likely to avoid mistakes. The nervous, quick-motioned impulsive individual will need to make deliberation a matter of study; else, when acting on the spur of the moment, with possibly slight embarrassment, ludicrous errors are liable to be made. In shaking hands, as an evidence of cordiality, regard and respect, offer the right hand, unless the same be engaged; in which case, apologize, by saying "Excuse my left hand." It is the right hand that carries the sword in time of war, and its extension is emblematic of friendliness in time of peace.
Fig. 1. The snob that sticks out two fingers when shaking hands.
Fig. 2. The cold-blooded, languid person, that exhibits only indifference as you shake the hand.
Fig 8. The generous, frank, whole-souled indivividual, that meets you with a warm, hearty grasp.