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Re: Mendoza's method for clearing lunars.
From: Frank Reed CT
Date: 2004 Aug 4, 13:51 EDT
From: Frank Reed CT
Date: 2004 Aug 4, 13:51 EDT
George H wrote:
"Then something funny happens. At the next value of lunar distance (which is 95deg) all the rows show a sudden jump in the value of the correction, by 20 seconds or nearly so, which is completely unphysical and could never happen in that way in real life. Then, as the lunar distance increases further, these values in succeeding columns gradually fall, in some cases to near-zero."
FWIW:
In Norie at the beginning of the tables, he has an explanation and description of each. For Table XXXV, after describing it generally and giving an example of its use, he writes:
"This table is somewhat altered from the original when the distance is above 90d (the seconds being the complement to 20 of those formerly given) in order to adapt it to an easy and general method of clearing the distance by Joseph de Mendoza Rios, Esq. F.R.S. When his method is used, the seconds are to be taken out with the apparent distance at the top or bottom, and the moon's correction and difference of corrections in the side column."
Also note that because of the cotangent of the distance in the calculation of this quantity, the quadratic term (table XXXV correction) is effectively zero for lunar distances between 78 and 102 degrees.
Frank R
[ ] Mystic, Connecticut
[X] Chicago, Illinois
"Then something funny happens. At the next value of lunar distance (which is 95deg) all the rows show a sudden jump in the value of the correction, by 20 seconds or nearly so, which is completely unphysical and could never happen in that way in real life. Then, as the lunar distance increases further, these values in succeeding columns gradually fall, in some cases to near-zero."
FWIW:
In Norie at the beginning of the tables, he has an explanation and description of each. For Table XXXV, after describing it generally and giving an example of its use, he writes:
"This table is somewhat altered from the original when the distance is above 90d (the seconds being the complement to 20 of those formerly given) in order to adapt it to an easy and general method of clearing the distance by Joseph de Mendoza Rios, Esq. F.R.S. When his method is used, the seconds are to be taken out with the apparent distance at the top or bottom, and the moon's correction and difference of corrections in the side column."
Also note that because of the cotangent of the distance in the calculation of this quantity, the quadratic term (table XXXV correction) is effectively zero for lunar distances between 78 and 102 degrees.
Frank R
[ ] Mystic, Connecticut
[X] Chicago, Illinois
