Mathematical Order of the Measuring Line


“Their line is gone out through all the earth, and their words to the end of the world” (Psalm 19:4).

The word line here is the Hebrew qav, which literally means measuring line, which biblical scholars see as a poetic description (modern translations use voice). However the experts choose to translate it, the stars actually do send out a type of “measuring line” throughout the whole world that has historically provided many useful, practical results.

Angle measurement also enables us to chart positions of the sun, moon, stars, and planets. An angle-based coordinate system exists in the sky, very similar to latitude and longitude on the earth. In the sky, declination measures angular distances from north to south, just like latitude on the surface of the earth. Right ascension measures angular distances in the sky from east to west, very similar to longitude on the globe. Just like on the earth, a celestial equator and celestial poles exist in the sky.

These celestial coordinates of declination and right ascension closely relate to the terrestrial coordinates of latitude and longitude. For any given latitude, the corresponding angle of declination passes directly overhead at the zenith. For example, at latitude 40 degrees north, the stars at declination 40 degrees north pass overhead. Many major United States cities are near latitude 40 degrees north, including New York, Philadelphia, Cleveland, Chicago, Denver, Salt Lake City, and San Francisco, and world capitals such as Madrid, Rome, Istanbul, and Beijing. All of these cities see the same stars directly overhead from night to night.

On the equator the stars of the celestial equator are directly overhead at the zenith, such as Orion’s Belt. At the North Pole, the North Star, Polaris, is at the zenith. For every location on the earth this mathematical correspondence enables an observer to find his latitude from the declination of the stars. This is the basis for celestial navigation. For centuries of preindustrial history, before the development of modern instruments such as GPS, navigators in wooden sailing ships could find their position from this mathematical order of the sky.

Since ancient times, sailors, using simple angle-measuring instruments such as a quadrant, sextant, and cross-staff have been able to measure the altitude of stars and learn their precise latitude while in the middle of the ocean. A basic quadrant is nothing more than a protractor with an attached plumb bob. One simply sights the star and measures the angle of its altitude from an inscribed scale. Relying on such simple devices, Columbus crossed the Atlantic to discover the New World, and the Pilgrims found their way to Plymouth Rock.

Finding longitude is a more complex procedure. The development of mechanical clocks in the eighteenth century made it possible to find longitude at sea. The mariner chronometer keeps an accurate measurement of the time at the homeport. Sailors carefully measure noon at their location at sea, when the sun is highest in the sky, and compare that to the time on the chronometer. The number of hours difference between the local ship time and the time at home helped the sailors discover the “time zone” that corresponded to their longitude. We use the same method today to define the twenty-four standard time zones of the world, each representing 15 degrees of longitude.

In addition to navigation, the art of surveying has historically used the same celestial angle-measurement techniques. English surveyors Charles Mason and Jeremiah Dixon used astronomical techniques to establish the Mason-Dixon Line, the border between Pennsylvania and Maryland. Andrew Ellicott used similar astronomical surveying methods to establish the border between Pennsylvania and Ohio, and the northern border of Florida. Ellicott and Benjamin Banneker, his neighbor and fellow astronomer, used spherical astronomy to survey the streets of Washington, DC. Similar astronomical techniques had been used to survey 1.8 million acres of land in the United States.

Jay Ryan is the author of Signs & Seasons: Understanding the Elements of Classical Astronomy, a homeschool astronomy curriculum, and Moonfinder, a book for every member of the family to learn how to follow the monthly cycle of the moon’s phases. Visit Ryan’s website at


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