How Did They Measure Lat & Long?

[carnivorousplant]

@Xema

Could you not also use the time that’s halfway between two times at which the sun’s altitude is equal? (The sunrise/sunset method being a special case of this.)

Why not do like that Greek fellow and look down a well? On a ship, down a tube, or watch the shadow of a mast?

[DPRK]

@Chronos

Oh, I should also mention that not all measurements are equal, where precision is concerned. For instance, multiple observations of the Sun for a little while before and after local noon will give you a pretty good measurement of your latitude, but a not-so-good measure of the time of local noon, because noon is when the altitude of the Sun is changing most slowly. Similarly, if you take just one measurement at what your clock says is noon, or when your compass-plus-correction says it’s due south, it won’t matter much if your clock or compass is a moderate amount off. If you want a really good measurement of the time of noon or of true north, then you want to use the sunrise-and-sunset method.

My post focused on the latitude, but I ought to have further quoted (from the chapter “To find the time at sea, and regulate a watch, by the sun’s altitude”):

The best method of obtaining the apparent time at sea, is by observing, by a fore observation, the altitude of the sun’s lower limb when rising or falling fastest, or when bearing nearly E. or W.; to this altitude we must add the semidiameter and parallax, and subtract the dip, (or, instead of these three corrections, add 12’, which will answer very well for an observation taken on the deck of a common-sized vessel;) subtract also the refraction, taken from Table XII., and the remainder will be the correct altitude. The ship’s latitude must be found at the time of observation by carrying the reckoning forward to that time. The declination must be taken from Table IV., or from the Nautical Almanac, and corrected for the ship’s longitude and the time of the sun from the meridian by Table V. […]

Having thus found the correct altitude, latitude, and polar distance, the apparent time of observation may be found by either of the following three methods…

So, indeed, Bowditch confirms that the sunrise-and-sunset method is best, unless you happen to be on shore and have an adjusted and collimated transit instrument.

[DPRK]

@carnivorousplant

Why not do like that Greek fellow and look down a well? On a ship, down a tube, or watch the shadow of a mast?

Transit. Not much use on board ship, though.

[Chronos]

Yes, any pair of times at equal altitude will work. But if the points are too close to noon, then your precision starts to degrade again.

And looking down a well will only work in the Tropics, and then only once or twice a year: The Sun usually isn’t directly overhead at noon; it’s just the closest to overhead that it’ll get.

[Chronos]

Oh, and to find the highest point, given a set of spaced-out measurements (where it’s possible that the highest point is somewhere between two of them):

Start by plotting your points on a page, and then put a diagonal line across the page. Copy your graph, and the line, onto a piece of transparent material. Flip the transparent page over, and overlay it on the original page. Slide the transparency left and right until the two sets of points line up on the same smooth curve. The intersection of the two diagonal lines now gives you the time of the highest point, at the center.

[DPRK]

@Xema

Could you not also use the time that’s halfway between two times at which the sun’s altitude is equal? (The sunrise/sunset method being a special case of this.)

Yes.

A chronometer may be regulated on shore by observing in the morning and evening the times when the sun is at the same altitude, [*The altitudes should be taken when the sun rises or falls fast. The best time for observation is when the bearing of the sun is nearly east or west, if the altitude exceed 8° or 10°, so as to avoid the irregular refraction hear the horizon. In general, two or three hours from noon will be sufficient…] for the middle between these times would be the apparent time of noon by the chronometer, if the declination of the sun remained the same during the observation; but if the declination varies, as is generally the case, the apparent time of noon determined in this manner… must be corrected for the change of declination by an equation… and the middle time thus corrected will be the correct time of apparent noon by the chronometer. For greater accuracy, several altitudes should be taken in the morning, and corresponding ones in the afternoon…

ETA anyone interested in the details of all this stuff should take a look at the book.

[Chronos]

OK, accounting for changes in declination of the Sun over the course of a single day is further than I would have gone. And if someone had told me I had to take it into account, I’d just do my observations at a solstice.

[Morgenstern]

All this seems so funny in a day when a 10 year old can whip out his cellphone and give you his current global position in seconds.

[carnivorousplant]

@Chronos

And looking down a well will only work in the Tropics, and then only once or twice a year: The Sun usually isn’t directly overhead at noon; it’s just the closest to overhead that it’ll get.

I thought that the definition of noon was when the sun was directly overhead.

[UDS]

@carnivorousplant

I thought that the definition of noon was when the sun was directly overhead.

How often do you observe the sun to be directly overhead in central Arkansas?

[carnivorousplant]

@UDS

How often do you observe the sun to be directly overhead in central Arkansas?

At noon, I thought.

[carnivorousplant]

How did 19th century navigators determine local noon?

[Chronos]

The best answer to that is to go outside at noon tomorrow and check.

But to provide more detail on what you’ll inevitably see, in central Arkansas, the noontime Sun will always be somewhere in the southern portion of the sky. It’ll be closer to directly overhead in June, and furthest from it in December, but it’ll always be a decent distance away (at least about 12 degrees).

The tropics are, by definition, those places where the Sun can be directly overhead: If you’re right on the Tropic of Cancer (23.5 degrees north), it’ll be overhead at noon on June 22. If you’re on the Equator, it’ll be overhead at noon on the equinoxes (in March and September). Right on the Tropic of Capricorn, it’ll be overhead at noon on December 22.

Or, to put it another way: At any given moment, there is always exactly one point on Earth (which will be somewhere in the tropics) where the Sun is directly overhead. In May through August, that point is in the Northern Hemisphere, and so the Northern Hemisphere gets summer. In October through February, it’s in the Southern Hemisphere, and so the Southern Hemisphere gets summer. If you’re north of the point where the Sun is directly overhead (which you always will be in Arkansas), then the Sun will be south of overhead.

How did 19th century navigators determine local noon?

Described above. They either first determined north, and looked for the moment when the Sun was directly south, or they looked at the times of sunrise and sunset, and found the moment exactly halfway in between, or some variant of those.

[carnivorousplant]

They could check their sundial.

[septimus]

@carnivorousplant

I thought that the definition of noon was when the sun was directly overhead.

Here’s a time-lapse video taken in late December in Fairbanks, Alaska. Does the sun make it all the way to zenith?

[carnivorousplant]

It is at the highest point at noon, is it not? So you watch it with a sextant. When it stops getting higher in the sky and begins to descend, it is noon?

[DPRK]

The zenith is a point directly above your head when you are standing, not to be confused with the whole meridian.

The book I mentioned gives many exercises instructive to see what is going on, e.g., in latitude 13° 17’ N, the sun’s declination being 22° 10’ S, in the morning the altitude of the sun’s lower limb was 36° 26’. What was the apparent time of the observation?

(If you work it out, do not forget to take into account refraction, semidiameter, and dip!)

This seems like the type of simple observation that would have been routine well into the 20th century, not to mention the 19th and long before.

[DPRK]

@carnivorousplant

It is at the highest point at noon, is it not?

Yes.

So you watch it with a sextant. When it stops getting higher in the sky and begins to descend, it is noon?

Your timing would not be very precise if you did it that way. How well could you mark the exact instant it stopped rising and began to descend?

A better idea would be to measure the altitude with a sextant in the morning or evening (or both) when it is rising/setting fast, as described.

ETA it should go without saying that, besides a sextant, you need a watch to time these observations…

[carnivorousplant]

@DPRK

A better idea would be to measure the altitude with a sextant in the morning or evening (or both) when it is rising/setting fast, as described.

How does it come to pass that marking noon is an important event in all those Royal Navy books?

[Chronos]

Because marking noon, and comparing it to the time reported by your shipboard clock that’s still set to Greenwich, is what tells you your latitude.