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George Huxtable wrote:

>Herbert says that "now" we all measure longitudes the same way, but if there 
>is any consensus, it's a recent one, dating from a IAU resolution in 1983, 
>and which has not been accepted by all; in particular, not by Meeus. 
>
George,

I understand why you don't accept a 25 year old resolution as proof of 
consensus. After all, the US had already voted 100 years earlier at the 
International Meridian Conference of 1884 for "east is positive" 
(resolution 4) - and then did not stick to it. Ironically, the German 
delegate considered the direction in which to count longitude an 
unimportant detail and declared himself unable to vote on it. Several 
countries followed him. It was the US delegate who insisted on settling 
this issue and voted for "E is +". Go figure... The proceedings can be 
found online in the Gutenberg Project.

While Newcomb is right with what he says about usage in the American 
ephemeris, Chauvenet is actually not the best witness for Meeus's cause. 
On p. 25, op. cit. below he defines longitude as the difference of  
simultaneously established right ascensions, namely of that of the 
meridian in question and that of the prime meridian. R.A. increases 
towards the east, doesn't it? On p. 317, Chauvenet speaks specifically 
of "west longitude". Indeed, west longitude runs west.

As long as trigonometrical computations were done with tables that 
covered a quadrant of the circle, the concept of negative angles was 
pretty unnecessary. One dealt with positive longitudinal differences, 
thereby distinguishing "cases" east and west. This has changed in the 
last twenty or thirty years. All computer programs dealing with 
navigation or mapping use cartesian coordinates at some stage, whether 
in two or three dimensions. The same is true for astronomy programs 
giving topocentric positions w.r.t. a reference geoid. As you say, at 
the presentation layer you can use E/W. (Not all programs do. For 
instance, the old MICA didn't.) After you have stripped off the 
man/machine interface you must make a decision as to how to represent 
E/W numerically. Your method must be consistent with other conventions 
such as how to display azimuth and it must be consistent with the 
trigonometric functions over the full circle. That given, it would be 
terribly inconvenient to use anything but "E is +, W is -". This cements 
a de facto standard which is independent of international conferences, 
much more compelling, and here to stay.

Herbert Prinz

>Meeus 
>provides several references about the matter, chosen, no doubt, to support 
>his case, which have sent me to my own bookshelves. The results may be of 
>interest. Here's what I've found, in chronomlogical order.
>
>Chauvenet, W, "A manual of Spherical and Practical Astronomy", 1891 (vol 1, 
>page 317), defining L, the difference of longitude between two points by 
>reference to their local times, states "L is the west longitude of the 
>point".
>
>Newcombe, Simon, "A Compendium of Spherical Astronomy", 1906, page 118, 
>says- "Astronomical custom is divided as to whether East or West longitudes 
>should be considered positive; the West are positive in the American 
>Ephemeris".
>
>"Explanatory Supplement to the Astronomical Ephemeris", 1961, refers on 
>page7 to a resolution of the International Meridian Conference in 
>Washington, 1884, one of its resolutions being- (referring to Greenwich) 
>"That from this meridian longitude shall be counted in two directions up to 
>180 degrees, East longitude being plus and West longitude minus". However, 
>it goes on to say- "Although the other resolutions are now in use, it has 
>been customary for many years in astronomy, but not in all other related 
>sciences, to treat west longitudes as positive and east longitudes as 
>negative. That is the convention adopted in the Ephemeris." And indeed, in 
>the ephemeris for 1971 and 1976, positions of observatories are given with 
>their longitudes marked as + or -, not W or E, and clearly the 
>West-is-positive convention is applied.
>
>However, following that IAU resolution in 1983, the author of the successor 
>to that Explanatory Supplement, Siedelmann, (1992) is in no doubt, saying 
>that longitude is "...measured eastward around the Earth from 0� to 360� 
>...". And indeed, my Astronomical Ephemeris for 1985 gives observatory 
>positions which are described, specifically, as "Easterly Longitude", with 
>the appropriate sign.
>
>That might be that, you would think, but for the rejection of that change by 
>the influential Jean Meeus, who points out, on page 93 of "Astronomical 
>Algorithms", that for all other planets, longitudes are measured in the 
>opposite direction to their rotation, but for some reason, not so for the 
>Earth.
>
>So there is hardly the clear-cut consensus that Herbert would wish for.
>
>George.
>
>  
>


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