Case in point: Williams's New-York Annual Register for the year 1834 includes "A TABLE FOR THE EQUATION OF TIME For Regulating Clocks and Watches for the year 1834" (p. 21). The column headings are the months of the calendar, and the row headings are the alternate days of the month (1, 3, 5, etc.). Each cell gives a number of minutes and seconds and either "fast" or "slo." At the bottom of the table appears the following explanation:
How to Set a Clock or Watch by the above Table. -- EXAMPLE. -- January 1st, I find by looking into the table, that the Clock to be right must be 3 minutes and 49 seconds faster than the Sun-dial : therefore, I set it so much faster. And so of the rest. -- Twelve o'clock is the best time to a set a Clock or Watch by a Sun-dial.
NOTE. -- A Sun-dial shows Solar or Apparent Time, but a Clock, &c. should be set to Mean or Equal Time, as the Table directs.
So clocks had to be adjusted every other day to be "right," that is, set to Mean Time; and, although it doesn't say so, one has to assume that this table was accurate only for the longitude of New York City.