In his next letter, the author referred to himself as "The Zodiac," and, again included the crossed-circle symbol. This symbol would continue to appear in almost all of the killer's authenticated communications.

The name "Zodiac" is derived from the Greek word "zodiakos," which, translated, means "a circle of animals." The American Heritage Dictionary (1983) offers the following definitions:

zodiac: n. 1.a. A band of the celestial sphere, extending about eight degrees to either side of the ecliptic (the sun's path), that represents the path of the principal planets, the moon and the sun. b. In astrology, this band divided into 12 equal parts called signs, each 30 degrees wide, bearing the name of a constellation for which it was originally named. 2. A diagram or figure representing the zodiac. Gk. zodion - small represented figure). zodiacal, adj.

The crossed-circle often represents a compass and the corresponding directions North, East, South and West. In relation to the astrological zodiac, the symbol is also used in this manner, or to denote the four seasons of spring, winter, fall and summer. The symbol also serves as the astrological notation for the planet earth.

The crossed-circle is also a fundamental symbol in mathematics, representing what the Cartesian Unit circle. Used in advance calculus and other mathematical applications, the Cartesian Unit is part of a system whereby points on a plane can be located by their "Cartesian coordinates" along the vertical, or y-axis, and the horizontal, or y-axis. The x and y axis divide the Cartesian plane into four sections, called quadrants. In the first, or upper right quadrant, all the coordinates are positive. In the second, or upper left quadrant, the x-coordinates are negative, and the y-coordinates are positive. In the third, or lower left quadrant, all the coordinates are negative. In the fourth or lower right quadrant, the x-coordinates are positive; the y-coordinates, negative. These quadrants read counterclockwise, and arcs on this unit circle are measured in radians.

On November 9, 1969, the San Francisco Chronicle received another letter from the Zodiac, which announced that the killer was going to change "the way the collecting of slaves" and complained that the police were "telling lies" about him. The author also spoke of his "masterpiece," which he called "the death machiene," and included a formula for an explosive in addition to a sketched diagram depicting such a device. At the end of this letter, the Zodiac had drawn a large crossed-circle, adding what appeared to be five small X's on the circumference of the circle at the left.

In June of 1970, the San Francisco Chronicle received one of the Zodiac's most mysterious pieces of mail. The envelope contained a letter, and a map of the Bay area. The letter featured another code which the Zodiac said was to be used in correlation with the enclosed map in order to determine the location of a bomb. The code consisted of 32 characters; some were letters of the alphabet and other were symbols found in astrology, mathematics, etc. Above this code, the Zodiac had drawn another crossed circle, and to the right, added the number 12.

On the map, the Zodiac had drawn a crossed-circle over Mt. Diablo, taking time to leave the center of the cross incomplete so that peak of the mountain was still visible. The cross was placed over the mountain in such a manner that the four points approximated the four points of a compass, and, at each of these positions, the Zodiac had written a number; North = 0, East = 3, South = 6, and West = 9. To the right of the zero were the following words: "is to be set to Mag. N."

This was an obvious reference to Magnetic North, defined as the direction to which the north-seeking pole of a magnetic compass needle points. The magnetic force of the earth pulls the compass needle out of alignment with true north. The difference between true north and magnetic north is the angle of declination, which varies according to the location of a compass on the earth. The angle of declination from Mt. Diablo is estimated between 16.5 and 17 degrees east of true North. The declination is occasionally adjusted as the magnetic force of the earth that causes the variation shifts and changes with the passage of time.

In another letter, the Zodiac included his largest crossed-circle, which covered more than half of a page. Below this, the Zodiac had written "PS. The Mt. Diablo code concerns Radians & # inches along the radians."

A radian is an angle valued between 57 and 58 degrees, or, 57.296, defined as "an angle subtended by an arc of a circle equal in length to the radius of a circle." The radian is the usual unit of measurement in higher mathematics, however, in applications of mathematics to surveying and navigation, the degree is more commonly used. The term "radian" is a contraction of the words "radius-angle." A circle, depicted by a circle within a circle in mathematics, consists of 360 degrees - 6.28 or 2pi radians.

In order to locate a bomb, it would be necessary to study the map and determine where to look for such a device. To identify that location using the code and "radians," geometric angles must be applied to the map and the geography it depicts.

The word "survey" is defined as determining and delineating the form, extent, position, etc., of, as a tract of land, by taking linear and angular measurements, and applying the principles of geometry and trigonometry. As noted earlier, navigators and surveyors measure radians by degrees in accurately determining the precise geographical locations on a map as well as on the earth itself. Therefore, if the radians are intended to indicate a geographical location, these radians would most logically be measured in degrees. The radians would somehow be located and marked on the map, possibly using both Mt. Diablo and Magnetic North as references. Once the radians were located on the map, it would be necessary to measure a number of "inches along the radians" in order to narrow the search for the location in question.

Of course, it would also be necessary to decipher the "Mt. Diablo code" to determine its true meanings and accurately place these radians on the map. However, the map itself may offer a clue indicating the placement of perhaps one radian.

The map illustrates the Bay area, including San Francisco, Berkeley, Oakland, and the southern portion of Vallejo. The border of this map falls just north of Lake Herman Road, which is clearly visible at the top. Blue Rock Springs Park, not visible on this map, would appear just above its northern border. The only other "Zodiac" crime scene visible on this map is the intersection of Washington & Cherry Streets in San Francisco, scene of the murder of cabdriver Paul Stine on October 11, 1969.

The Zodiac sent a Halloween card and, on the back, he wrote the words "paradice" and "slaves" to form a cross, and in the four quadrants created by the cross he added the words "by gun, by knife, by fire, by rope." The two scenes visisible on the Zodiac's map marked the first and last known Zodiac murders, and the killer used a gun in both crimes.

The Zodiac annotated the map using a blue felt-tip pen that rendered a rather thick line. When such a pen is used to draw straight lines from the scene of the Lake Herman Road shooting to Mt. Diablo, and from Mt. Diablo to the intersection of Washington and Cherry Streets, an angle valued somewhere between 60 and 61 degrees is formed. Another straight line from Mt. Diablo to the scene of the Blue Rock Springs shooting (or where it would appear were it visible on this map) falls somewhere between 57 and 58 degrees, approximating a radian angle.

This radian may be the result of coincidence, but, given the Zodiac's instructions, it is possible that the angle pertains to the larger solution to the code and map mystery. Until someone discovers an accepted solution to the coded message, the Mt. Diablo map and code, along with the radian clue, will remain the subject of confusion, frustration and debate.