100 r ^d
[1] a = (c - 100) +   ___________
                                     r ^d - (r - g)^d

where c is the full ring count of a partial increment core; g is the length of the innermost 100 rings of the increment core; r is the length g plus the length of the section of bole radius (extending to the tree's pith) that was not sampled by the increment core; and d is given by the following equation:

[2] d = 0.230 + 0.759(100/g_mm) + 1.27r - 0.848r² + 0.159r³

Units for g and r are meters, whereas g_mm is the length of the innermost 100 rings of the increment core in mm. For reasons discussed in Stephenson and Demetry (1995), if r exceeded 3 m, r = 3 m was substituted into eq. 2 for calculating d.

A sequoia's pith usually is not at the geometric center of its bole. However, we typically have no way of determining the location of a living tree's pith, and therefore cannot directly measure the value of r associated with a particular increment core. Therefore r was estimated as described by Stephenson and Demetry (1995). First, tree radius was calculated as half of tree diameter (determined by diameter tape) at the height at which the increment core was taken. Average bark thickness, determined by probes at several location around the bole, was then subtracted to determine tree radius inside the bark. From this, the length of the increment core, excluding the core's innermost 100 rings, was subtracted, yielding an estimate of r.

Because increment cores shrink as they dry, the wet length of a core must be known for the most accurate application of eqs 1 and 2. However, for most of the sequoias analyzed here (the Sentinel tree being the one exception), wet lengths of cores were not recorded. My colleagues and I (unpublished data) have found that the average shrinkage of hundreds of sequoia cores was about 2%. Thus, when the wet length of a core was not recorded, it was estimated by multiplying the core's dry length by 1.02.

To improve accuracy, when several cores were available from a sequoia, a given core's location on the bole had to be separated from that of the other cores by at least 90E of circumference to be included in the age estimation (Stephenson and Demetry 1995). Tree age at height cored was estimated by averaging the age estimates based on the individual cores (Stephenson and Demetry 1995).

Some of the data used to estimate sequoia ages came from sequoias cored several decades ago. It was therefore necessary to account for the number of years that have passed since a sequoia was cored. Because, for convenience, I wished to estimate all sequoia ages relative to the year 2000, I subtracted the year in which a core was taken from 2000, then added the result to estimated tree age.

The method outlined above only estimates sequoia age at the height at which the cores were taken. However, accounting for the time it took a tree to grow to the height cored potentially can add decades to the tree's estimated age. To account for height growth, I multiplied the height of the core above ground level (in m) by 178x ^-0.957, where x is the (estimated) cumulative width, in mm, of the 10 rings that abut the tree's pith. This empirical factor scales height growth to radial growth, and was derived from ring measurements of 41 smaller sequoias which my colleagues and I cored to the pith both near ground level and near breast height (see Agee et al. 1986 for a similar approach). However, because there is no way of knowing the actual cumulative width of the 10 rings that abut the pith of the large sequoias analyzed here, I assumed that the width was 27.5 mm, based on the average from measurements of more than 450 sequoia stumps (Table A in Huntington 1914). Thus, I assumed that large sequoias took 178×(27.5)^-0.957 = 7.5 years to grow each meter taller until core height was reached. However, with the exception of the Sentinel and Grizzly Giant trees, core heights were not recorded. I therefore estimated core heights for the other trees based on conversations and correspondence with individuals involved in the corings (H. S. Shellhammer for the General Sherman, Washington, General Grant, and Cleveland trees, and R. Adams and L. Mutch for the Boole tree).