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Re: Origin of the analemma
From: John Huth
Date: 2011 Oct 13, 18:29 -0400
Interesting.

I'm assuming that the classic analemmas on globes are either time averaged or the resolution is too poor to see differences in the year-to-year variations.   If you draw them large enough, the year-to-year variations begin to become apparent.    I tried to play with some time averaging to get a quick-and-dirty scheme for calculating solar declination that was decent for any year.   By averaging and a trapezoidal approximation to deviations from a sinusoid, I got a precision of about 10 arc-minutes, but it's tough to push past that on a time average.

Another interesting question to contemplate is the following:  "what do an analemmas" look like on other planets?   It turns out there are curious variations, depending on the planet.

John H.

On Thu, Oct 13, 2011 at 4:52 PM, Frank Reed wrote:

Herbert Prinz once noted that the "analemma" is a weird name for that figure-eight shaped graph of the equation of time versus the Sun's declination that we're all familiar with. In line with my story about the International Date Line a few months ago (an invention of a globe maker in New York in the 1870s), it turns out that this, too, was a name invented by a globe manufacturer, this time c. 1770 or earlier in England.

Up until the late 18th century, the word analemma was used in most European languages to refer to a carefully drafted diagram or an engraving of the coordinates of the globe projected onto a plane in a standard orthographic projection. And that's all it meant. This "analemma" was used to solve approximately a variety of problems in spherical trigonometry on the globe (but without an actual globe) such as figuring out rising and setting times at selected latitudes. If you look for this word through Google Books for years before about 1770, it always refers to this diagram of an orthographic projection.

Starting sometime around 1770, an author and globemaker, Joseph(?) Harris began adding a "slip of paper" to globes which displayed the declination of the Sun for every day of the year aligned with the appropriate latitude on the globe. And apparently he called this his "analemma". It, too, could be used to solve a variety of simple problems in spherical trigonometry such as figuring out rising and setting times, and it seems that he may have chosen the name by functional analogy. It does the same thing as the analemma as originally understood (the orthographic projection). But at first, this analemma was not the figure-eight diagram. That variation was added by another English globe manufacturer named Cary apparently in the late 18th century. Two kinds of analemmas, labeled as such, persisted on globes right through the beginning of the 20th century. There was the common figure-eight that graphed the equation of time versus declination which we still have today. There was also the earlier version which was a simple oval that displayed the declination and also the Sun's ecliptic longitude and zodiac sign.

The figure-eight analemma was not common in the literature of astronomy or navigation. It was seen almost exclusively on globes and apparently called an analemma primarily in English through the early 20th century. But just to be clear, the concept of the equation of time, its values, and the corresponding declination of the Sun have, of course, been known since antiquity. And the figure-eight diagram combining the two was apparently first displayed sometime in the early 18th century though it was not called an analemma. In French it was the "meridien du temps moyen" or the "meridian of mean time" which is, in fact, a very accurate description of what it implies about the Sun's motion: at noon as indicated by a mean time clock, the Sun will trace out that path during the course of the year. The diagram was popularized and NAMED the analemma by those English globe makers over 200 years ago, perhaps by analogy with the earlier diagram called an analemma. Finally, sometime in the second half of the 20th century, the modern meaning of the word analemma went international, and it now is applied almost universally to the graph of the equation of time versus the Sun's declination through an average year.

Here's a description of the evolving meaning of the word analemma as of about 1812 from Keith's treatise on globes:
"The Analemma is properly an orthographic projection of the sphere on the plane of the meridian; but what is called the Analemma on the globe, is a narrow slip of paper, the length of which is equal to the breadth of the torrid zone. It is pasted on some vacant piace on the globe in the torrid zone, and is divided into months, and days of the months, correspondent to the sun's declination for every day in the year. It is divided into two parts; the right hand part begins at the winter solstice, or December 21st, and is reckoned upwards towards ths summer solstice, or June 21st, where the left hand part begins, which is reckoned downwards in a similar manner, or towards the winter solstice. On Cary's globes the Analemma somewhat resembles the figure 8. It appears to have baen drawn in this shape for the convenience of showing the equation of time, by means of a straight line which passes through the middle of it. The equation of time is placed on the horizon of Bardin's globes."

-FER

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