Another special one. In this chart we have two LCD's--the first is #60 at 11.9 ru, and the second is #68 at 18 ru. First we have #60 (11.9 ru) with #103 at 47.8 ru (4 x11 .9 = 47.6). Next we have #7 at 23.6 ru (2x11.9=23.8) as a counterbalance to #103. Next we see that #68 at 18 ru is one-half the distance of #83 at 36.1 ru. At almost a right angle, we find #20, which is also 36.1 ru. Could there be any other linkage between #20 and #83 besides their common distance from #37? The distance between these two points is 48.5 ru, which gives us a triangle with the length of each leg evenly divisible by 12, to give a ratio of 3:3:4 for the sides. Before we let go, we can see that #20 is 30.6 ru . from #7. Perhaps, the LCD for this set should be considered as 6 since 12 and 18 are both divisible by 6. We now see that the triangle formed by #7, #37, and #20 has sides in the ratio of 4:5:6.

In this one we have an LCD of 5.3 ru, established by #39 and #28. In a nearly straight line with #39, we have #75 at 26.4 ru (5 x 5.3 = 26.5) and #6 at 32 ru (6 x 5.3 = 31.8). #46 at 26.5 ru (5 x 5.3)is opposite to #30 at 16.2 ru (5 x 5.3 = 15.9). #30 (16.2 ru) is opposing #51(31.8 ru). This leaves us with #55 at 21.3 ru (4 x 5.3 = 21.2) and #103 at 47.8 ru (9 x 5.3 = 47.7).

The strong point on this chart is #34 at 7.7 ru in a nearly straight line with #26 at 23.1 ru (3 X 7.7). We have the obscure and uncertain point of #62 also at 23.1 ru, as a matter of curiosity. Then we have #59 (15.4 ru) counterbalanced by #12 (15.3 ru). We find #17 at 15.2 ru is nearly doubled at #4 with 30 ru. Lastly, #59 (15.4 ru) is tripled at #97 with 46.1 ru.

The first special feature on this chart is the two remnant highs #65 and #27 counterbalancing each other in a nearly straight line with the exact distance of 18.1 ru each. The second special feature is that the centers of #60, #70, and #81 all lie in a nearly straight line with their distances at 8.9 ru, 17.7 ru (2 x8.9 = 17.8) and 35.7 ru (4x8.9=35.6) .

This one has what seems to be an LCD of approximately 10.7 ru. The two points,#86 at 21.3 ru and #89 at 21.5 ru (2 x 10.7 = 21.4), are counterbalanced by #4 (32.1 ru) and #5 at 32.2 ru (3 x 10.7 = 32.1). A very slightly discordant note in this melody is #59 at 10.5 ru, instead of the apparent LCD of 10.7 ru.

The unique feature of this chart is #58 at 12.5 ru--nearly in a straight line with #9 at 37.4 ru (3x12.5=37.5). We also see that #52 at 25 ru is twice the distance of #58. We finally have #29 hanging in there at 12.2 ru.

This chart is for general interest only since we are using #4, #5, and #13 (three obscure points). The LCD is approximately 8 ru. The triangle formed by #39, #42, and #13 has three sides in the ratio of 7.9:16.1:16.7 which is approximately 1:2:2. The triangle formed by #39, #5, and #13 has three sides in the ratio of 16.1:24.8:32.2, which is closely 2:3:4.

This pattern, with an approximate LCD of 10.1 ru, looks like a rake, with a handle represented by the ray to #49. #30 and #65 are in the 20 ru range, and #11, #90, and #49 are in the 30 ru range. Perhaps #11 should be left out in view of its obscure and indefinite location, but it was entered for completeness.

The special feature on this chart is #86 (23.6 ru) and #51 (23.4 ru), with the distance between them at 32.3 ru. This arrangement gives us a triangle with sides in the approximate ratio of 3:3:4 (using 8 ru as the common denominator). To add an additional twist, we find that the angle between the two rays is 47.2 cu (which is very nearly twice the numerical value of the two common legs). If we exactly double the distance in a straight line out from #86, we find #102 at 47.2 ru. Now this point must be considered as highly questionable in location, but the distance between #102 and #81 is 23.7 ru. This gives us a triangle formed by #40, #81, and #102 with the length of the sides as follows: 23.7 ru (2 x 11.8 = 23.6), 35.2 ru (3 x 11.8 = 35.4), and 47.2 ru (4 x 11.8), respectively--an almost perfect ratio of 2:3:4.

The refreshing feature of this chart is #60 at 12.8 ru, which is doubled by #89 at 25.7 ru, both of which are in a straight line. #76 and #49 at 25.8 ru join with #89 at 25.7 ru, to form a partial ring. #99 at 39 ru (3 x 13) seems to have taken an , LCD that is the average between the 12.8 ru of #60 and the 13.2 ru of #55.