Beating eggs, especially beating egg whites to a stiff peak, was a labor intensive process prior to the universal use of the patented egg-beater. To lessen the strain on the arm, the cook was told to acquire the habit of beating eggs from the elbow, not using the whole arm. – The American Domestic Cyclopaedia. 1890. NY.
Persons who do not know the right way, complain much of the fatigue of beating eggs, and therefore leave off too soon. There will be no fatigue, if they are beaten with the proper stroke, and with wooden rods, and in a shallow, flat-bottomed earthen pan…In beating them do not move your elbow but keep it close to your side. Move only your hand at the wrist and let the stroke be quick, short, and horizontal; putting the egg-beater always down to the bottom of the pan, which should therefore be shallow. Do not leave off as soon as you have got the eggs into a foam; they are then only beginning to be light. But persist till after the foaming has ceased, and the bubbles have all disappeared. Continue till the surface is smooth as a mirror, and the beaten egg as thick as a rich boiled custard; for till then it will not be really light. It is seldom necessary to beat the whites and yolks separately, if they are afterwards to be put together…When white of egg is to be used without any yolk…it should be beaten till it stands alone on the rods; not falling when held up.
Hickory rods for egg-beating are to be had at the wooden-ware shops, or at the turner’s. For stirring butter and sugar together, nothing is equal to a wooden spaddle. It should be about a foot long, and flattened at the end like that of a mush-stick, only broader. – Leslie, Eliza. Miss Leslie’s Lady’s New Receipt-Book. 1847 and 1850. Philadelphia.
There were other authors who disagreed with not separating the whites and yolks although that meant more work in beating them a separately.
Instructions were also to always beat eggs in only one direction. – Archaeological Institute of America, Southwest Society. Out West. May 1911.
This is best done with rods of wood in a shallow, flat-bottomed pan; bestow the beating with short, quick, downward strokes, without moving the elbow, which should be kept close to the side. When the foaming and bubbles disappear, and the beaten eggs assume the appearance which has been well described as that of a rich boiled custard, your task will have been very well accomplished. Kent’s egg-beater is an excellent little instrument which greatly facilitates this process. – Cassell’s Household Guide. 1869. London & NY.
Beginning in the 1850’s, a string of patents were granted for various improvements to the egg-beater, continuing into the 20th century, yet every household did not have one even into the 1920’s, as evidenced by the number of cookbooks which instructed the cook to use a fork to whip eggs when no egg-beater was available. – U.S. Congress. House Documents Otherwise Published as Executive Documents, 13th Congress.
An earthen basin is best for beating eggs, or cake mixture…Eggs should be beaten with rods, or a broad fork…- Jewry, Mary. Warnes Model Cookery and Housekeeping Book. 1868.
Louis-Eustache Audot recommended a tinned beater over rods claiming that the wooden rods broke and sometimes left splinters in the eggs or other matter being beaten. The model he illustrated had several wires coming out of a round tin handle, the wires all being fixed in a flat row. – Audot, Louis-Eustache. French Domestic Cookery. 1846. NY.
The Dover egg-beater cost ten cents in 1886 and, “answers to all purpose of a more expensive cream-whipper, besides being a standard egg-beater for all purposes.” The Dover egg-beater  was a patented improvement (adding a second rotating whisk) to an existing beater that had only one rotating whisk. – The Cottage Hearth. April 1886.
Whipping cream or beating egg whites without a rotary beater is a hard slow job. I’ve often passed the bowl around the table asking each person present to spend a few minutes operating the whisk in order to have whipped cream for a dessert. What great grandma wouldn’t have given for my electric stick blender!