that rises one point for every two time periods will be referred to also, and this rise over run method will be use throughout this book in reference to angles.

These geometric angles not only offer support and resistance on the chart, but also, measure space and time periods, or in other words, they do mathematical and geometric calculations. This is substantially easier than calculating these prices and times mathematically, and it will also allow you to visually see the prioe levels and time periods.

There are three angles of major importance. The 2X1 moves up or down at 2 points per week or month. The 1x1 or 45 degree angle, whioh is the most important, accurately measures time periods as in the square of the range. The slower 1X2 moves at half the rate or one point every two weeks or months. Other angles that are used are 3X1, 4X1, then 8X1 whioh you will only use during very rapid extended moves or on daily charts. These angles then give you a visual idea of the type of momentum the stock or market IS developing. The 3X1 angles are used primarily on monthly and weekly charts.

There are a few points about the anoles which should be covered now. First of all, the angles are drawn from major highs and lows, with the angles moving down from highs, and up from lows. Angles from the highs represent resistanoe areas, although, they can afford support if price is at a harmonic to time. Angles up from low give support. Angles from high and low points in price are very important to the resulting move from that low or high. But. angles drawn up from zero, from the date of major lows and highs on the chart are, also, very important to this work.

In and of themselves, the angles are helpful to trading but do not stand on there own as support and resistance levels. They may be a trigger to a trade. On a daily chart, these angles may be broken early in a drive and then recovered, whioh would be a buy indication. But, if support is shown on a fast angle you could expect a fast move in that direction. On Weekly and Monthly charts, the angles can be exact support and resistanoe and should be monitored at all times.

The following is an excerpt from instructions Gann gave concerning angles:

"It IS not necessary to draw angles from a long way back. You can make the calculation and determine where they cross. For example: Suppose in 1900, in the month of January, a stock made bottom at 15, and I want to calculate where the 45 degree angle will cross 20 years later in January, 1930. The 45 degree angle rises at the rate of 1 point per month. Then 10 years would be 120 months or 120 points added to 15 at the bottom; the 45 degree angle would cross at 135 in January, 1930. All of the other angles may be calculated in a long way back the same way.

From any bottom, base or beginning point, two 45 degree angles can be started, one running up from the vertical angle and one running down from the vertical angle. You can also use a 45 degree angle or any other angle from any top, running the 45 degree angle

down from the top, which indicates a decline of 1 point per month, week, or day, according to your scale of prices; then running the 45 degree angle up from the topj which would indicate a gain of 1 point or 1 degree per month.

For example: Take the low cf U.S. Steel on November 13, 1929, when it sold at 150. Start the 45 degree angle up and it gains 1 point per month; then start the 45 degree angle down from 150 and the stock has to decline 1 point per month to rest on the angle of 45 degrees. November, 1930, was 12 months from November 1929, and Steel made low at 138, which was on a 45 degree angle from bottom at 150 on an even time cycle. In December, 1930, Steel made as extreme low of 134 3/8. This was 2 points under the 45 degree angle from 150, but rested on the angle of 2X1 from the low at 111 1/4, made in January, 1927. In December, 1930, Steel closed above the 45 degree angle from the bottom of 150. As long as it stays above this angle, it is in a stronger position, but to regain the strongest ppsition, it will have to cross the angles of 45 degrees from 150 on the up side and stay above this angle.

Remember that when any stock breaks under the 45 degree angle on a daily chart, weekly or monthly puts it in a very weak position and indicates a decline to the next angle. However, when a stock can regain the 45 degree angle, it is in a stronger position. The same rule applies to a 45 degree angle up from any top. When a stock crosses the angle on the daily, weekly or monthly and stays above the 45 degree angle, it is in a very strong position. After a stock once drops below or gets above any important angle and then reverses its position by getting back above the angle or dropping below it, it changes the trend again.

The angles on the Monthly and Weekly charts are, of course, of greater importance than those on the Daily charts, because the daily trend can change quite often, while only the major changes are shown according to the angles on the monthly high and low and weekly high and low charts.

Always consider the distance a stock is from its base or beginning point when it breaks any important angle or crosses any important angle. The farther away from the base, the more important the change in trend, whether this be crossing an angle from the top or breaking under an angle from the bottom.

There are three important factors to consider, price, time and space movements. For example, when the price reaches 45, it meets resistance because it is equal to a 45 degree angle. Then when the price beaks a 45 degree angle, regardless of whether the price is at 45, 67, 90, 135, 180 or anywhere else, it weakens the position and equals a resistance angle, but is more important when a long ways from base. The distance the stock breaks the angle of 45 degrees or any other from the base is the most important. For example, many times a stock will rest on the angle of 45 degrees in its early stages when advancing, then later in reaction rests on it again, then have a prolonged advance, react and rest on the 45 degree angle again, and then hit a higher level, break the 45 degree angle the fourth time, which places it in an

extremely weak position because it is so far away from the base and so much time has elapsed since the stock made low level. Reverse this rule in a bear market or a decline and dont forget to consider that the monthly and weekly high low charts are the most important when angles are broken. Daiiy charts oan break angles and reoover them and it is impossible for a daily high and low chart to maintain an angle of 45 degrees for a very long period of time exoept when the final grand rush comes at the end of a big bull campaign."

Fast angles such as the 2X1 or 4X1, if valid support or reeistanoe, will yield fast moves. This is very true on weekly and monthly charts. Im sure you have seen those moves which start from a saucer bottom, where each low fails to move down to the previous trendline and actually starts a higher ascending trendline. If you took those situations and applied angles, you would find that the ascending trendlines are really ascending angles of the next higher degree. Usually breaking the fourth asoending trendline indicates the trend has changed.

Angles from zero, originating from the dates of major lows and highs, are very significant. Tnese must be on all weekly and monthly charts. Gann emphasized the importance of these angles starting from zero, and anyone who has etudied those angles will find the reason to be obvious.

PRICE SQUARES

One idea that I am certain has caused a good deal of confusion among individuals who are early in their study of Ganns work, is the idea of squares. Gann referred to cyclee as squares, and the squares which he used were geometric squares, that is, Just a plain square drawn on a ohart with four equal sides. This is not a number multiplied by itself. The equares whioh Gann used, besides those of the msjor time cycles, were the square of the high, the square of the low, and what Gann considered his most powerful tool, the square of the range. These three squares or cycles are all based off of price movement.

A fully constructed square is a very complicated piece of art work which consists of the square iteelf, and all of the angles which Gann used radiating from the top and bottom left hand corners. Following thie, the divieione in time are merked with vertical lines, and in price, the divisione are marked with horizontal lines (remember Gann referred to theee also as angles). These divisions are, in both price and time; 1/8, 1/4, 1/3, 3/8, 1/2, 5/8, 2/3, 3/4, and 7/8.

Gann used these squares for timing and to find horizontal divisions in price at which to expect support and resistance. He said that you could look for change on every one of the divisions in price and in time. But, if you do that, you are spending a considerable amount of time. Other than midpoints, I have never had any confidence in the divisions, alone, as a tradable setup.