METHOD OF ESTIMATING RAINFALL BY GROWTH OF TREES. 115 



1. A 5-year smoothed curve was made of the tree growth (expressed in millimeters). 

 This gives us the term - ' - in the reversed formula Rn = gg^^^ • Tn 



250-4 



2. This term is multiplied by 1,000, reduced to inches, and 3.GAf subtracted, 



leaving A„in inches. 



3. From A,,, an approximate R,, is found by the formula Rn = M + An — An-i 



4. This series of approximate rainfall, Rn, is smoothed and becomes the (S„ of the 



formula. 



5. Final values are then found by the proportion: , — r — : Sn '■ : T„ : R„ 



It should be emphasized that the above formula for conservation is the one found to 

 apply under dry climatic conditions. In moist climates the trees, so far as observed, seem 

 to depend on other meteorological elements or combination of elements. 



The Prescott trees, as we have seen, even without correction, give a record of rain- 

 fall with an accuracy of about 70 per cent. It is likely that the Flagstaff trees, with their 

 higher elevation, more certain rainfall, and more central location in the zone occupied by 

 tliis species, give somewhat more accurate records. They are probably much less often 

 subjected to extremes of dryness which throw the tree out of its equilibrium, and cause it 

 to produce an abnormally small set of rings. It seems likely, also, that the less porous and 

 less conservative soil, combined with a more abundant precipitation, jiroduces a yearly 

 growth more nearly pi'oportional to the rainfall than at Prescott. 



THE FLAGSTAFF 500-YEAR CURVES. 



Previously in this chapter, we have endeavored to determine the exact relation between 

 growth and rainfall and to ascertain the most accurate method of obtaining results. We 

 shall now apply these conclusions and methods to the oldest available trees. For this 

 purpose 19 of the Flagstaff sections were selected and were subjected to minute examination 

 and cross identification, in order, so far as possible, to eliminate all errors due to the omission 

 or doubling of rings. For convenience in handling the sections, each one was reduced to 

 a strip of wood extending from center to bark. The best of these was adopted as a standard. 

 It was then compared with each of the others, ring for ring, for 300 years. In this long 

 period only 9 years required a second examination, and only one reciuired a third. This 

 was the ring for 1821, which was often merged with that for 1822. The 2 rings appear 

 as one in 10 sections and as 2 in only 9 sections, but in many or most of the cases where 

 2 appear, they were so distinctly separate that they were counted as representing 2 years. 

 This is not aboslutely certain, however, and thus there may be an error of one year in 

 the portions of the curve of growth before 1821.* So far as is known, there is no probability 

 of any other error. In order to show the value of cross-identifying the rings of one tree 

 with those of another, Table J has been inserted on page 330 of this volume. It 

 shows the errors of identification in the original measurements of 1906, when the same sec- 

 tions were reviewed in the light of later knowledge. The table shows the exact errors 

 made in the original, straight-away counting, both in the number and place of the rings. 

 It is pubUshed here, partly, because it corrects the various errors in the sections of corre- 

 sponding number as they appear in the Monthly Weather Review for June 1909. 



In studies Uke the present, it is manifestly desirable to carry the curves of growth as 

 far back as possible. Only a few trees go back to an age of over 300 or 400 years, but 



* Subsequent comparison with historical records supports the identification here adopted. The data, however, were 

 not obtained in time to lie incorporated in this vohime. 



