148 



THE CLIMATIC FACTOR AS ILLUSTRATED IN ARID AMERICA. 



the true maximum and the true minimum. Expressed in general terms this means that 

 if half of the trunk has the full number of rings, and if the number diminishes regularly 

 to a minimum at a single point, an average measurement will be less than the maximum by 

 one-fourth of the difference between the maximum and the minimum. 



Suppose now that two radii be measured and that the angle between them l)e 180°— 

 that is, suppose that they lie opposite one another; in this case one of the radii will always 

 have a value of 100, so that the average value of the apparent maximum will be equal to 

 the true maximum. The value of the minimum, on the other hand, will fluctuate between 

 100 and 76, and its average will be 88. 



22.5 



Fig. 34.— Ideal Diagram to Illustrate tlie Dropping of Ring.'^. 



In actual practise, where two measurements are taken, it is not possible to have them 

 in line with one another. This is due to the fact that the trees, as has abeady been ex- 

 plained, are not sawed entirely, but are chopped through half their thickness. Only the 

 sawed part can be measured with ease and accuracy. Hence, in the choice of places for 

 measurement, we are limited to 180°. The distance of the radii from one another varies 

 from 90°, or occasionally even less, up to 180°, according to the exigencies of the trunk in 

 question. On an average, the distance is about 135°. In such a case, it is evident that 

 the two radii will be equal when they lie anj-where in the portion of the tree A^A^A^ or 

 in the positions XO and YO at a distance of 22.5° from the line where the number of rings 

 ceases to be the maximum. Evidently the maximum line can never lie in the sector of the 

 tree, 135° in extent, between X and Y] but must lie somewhere in the sector XA-Y. This 

 part consists of 180° having a value of 100 and 45° whose value ranges from 100 to 94. The 

 average value of this latter portion is 97. Therefore, the average value of all the maximum 

 radii which could possibly be obtained when the two radii are 135° apart would be 99.4. 



The value of the minimum radii may be calculated in the same way. Manifestly, the 

 minimum can never lie in the portion of the tree MA'-N, but must lie in the portion 

 MBN. The average value of this latter portion amounts to 90.4. The difference between 

 the average maximum and the average minimum readings is 9, which is 9 per cent of the 



