2 articles for "Logarithms"

Literally exponents.

They enable multiplication or division to be done by simple addition and subtraction. There are many types of logarithms, the most familiar being those devised by Briggs and Napier; but, the type most used by astrologers is called Diurnal Proportional Logarithms. A table of these is often found in ephemerides. They are used to simplify the task of interpolating between the tabular values to find the planetary positions for a specified time.

(This is now routinely done by use of pocket calculators or computers.)

See also:
♦ Interpolation ♦ Ephemeris

Proportional parts of a quadrant, expressed in numbers, whereby calculations of the planets' places at a given hour, or the Arc of Direction for a given date, can be made by simple addition and subtraction rather than by multiplication or division. They were invented in 1614 by Baron Napier of Murchiston for use in his astrological calculations. Tables of Logarithms are in common use in all schools by students of trigonometry. Tables of natural, proportional and logistic logarithms are also available, each designed for different uses. An improvement in logarithms was introduced by Henry Briggs in 1624.

The astrologer uses Diurnal Proportionate Logarithms in making numerous calculations, but their average usc is in calculating the planets' places for a given birth hour. Under Planetary: Motions, there are tables reducing daily motion to hourly motion, but if it is desired to do this by the use of Logarithms, proceed as follows:

Subtract the positions of the desired planet on two successive days to determine its daily motion. Also compute the elapsed time between your birth moment adjusted to local mean time, and the previous noon or midnight – dependent on whether your ephemeris for that year gives noon or midnight positions.

Suppose you are seeking the Moon's position for an elapsed time of 7h 35m on a day in which its daily motion is 14° 27': In the tables, select the column with 14 at the top; run down the column to 27; and set it down; also for 35 in the 7 column; thus:

Looking for this in the tables you would (Apolo Note: there is a huge logarithm table in the original book which would take impossibly long to reproduce - sorry!) find .72061 at 34 in the 4 column: 4°34'. Add this to the Moon's longitude on the previous noon or midnight, and you have the position for the desired moment. In the case of a planet, note whether it is retrograde, in which event the distance of travel during the elapsed time is subtracted from the previous noon or midnight position.

Verify all Data.
When adjusting the planets' places for a given birth moment, cultivate the habit of forming a mental approximation of the intermediate position for a given interval of elapsed time, before you verify it by a calculation. Comprehension of what you are doing is superior to the mere following of a formula. Also bear in mind that exact calculations to an approximate birth moment, or one that is not authentic and precise, is like holding a stop watch on a race when you do not know where the starting line is located. Whoever said "time is of the essence" should have been an astrologer. Is this date before standard time was used in that community? If so, what zone? Is that a Julian or a Gregorian date? Did they observe Daylight Saving Time at that season of the year? These are only a few of many questions that involve discrepancies amounting to hours - so what matter items which at most involve minutes, perhaps only seconds? Exact work is to be admired, but not in trying to make a silk purse out of a sow's car. Verify the authenticity of your data first. If you cannot do that, insert only even degrees, and interpret on the basis of Solar Houses.

See also:
♦ Interpolation ♦ Ephemeris