Surely the whole business of finding the solstice is like a slower analogue of finding noon by observing solar altitude?
Just around noon the altitude changes extremely slowly, and it is hardly possible to judge the time of maximum altitude exactly. Here, today, noon is at 12:04:49 but even if we take 20 minutes before and after then the Sun will only be 8 minutes of arc lower. 1/365 of a day is about 4 minutes, and that interval either side of noon will see the Sun lower than its noon altitude by roughly 8 * (4/20)^2 = 0.3 minutes. I am neglecting change in declination, which is insignificant so near the solstice. Hence the benefit of taking altitude sights at known times some significant time either side of noon and calculating the instant of noon from those. Even if the times are only known by a clock which may not be correct, the result is noon as shown by that clock, which can thus be corrected. Conversely, if the clock is trusted, the longitude can be found. In general, one would allow for the rate of declination change for the day and its effect on the two readings. Similarly, by analogy, we see the advantage of taking declination readings (by whatever means) on noted dates a few days either side of the solstice. Andrew James
