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some of these great trunks and making an actual count of the rings. This, however, it was impossible to do in what remained of the vacation.

Nevertheless it seemed that the data already secured should furnish sufficient basis for a good approximation to the answer desired. Of course no simple scheme of proportionate increase as between age and diameter would avail, since age increases regularly by addition of equal increments; whereas increase of diameter is by unequal increments, greatest at a point very early in the life of the tree, and diminishing thereafter to the end. The Glen Alpine tree, for example, could not by any possibility have doubled its diameter of 16 inches in twice its 230 years of age. Still less could it have doubled that again to 64 inches at 920 years of age. Yet this last diameter-by no means extraordinary among mountain junipers—could hardly have been reached short of 1400 or 1500 years!

Thus there was opened up for these trees a vista of life unexpectedly long, equalling perhaps even that of the giant sequoias. My thoughts turned at once to a study made many years ago of a magnificent specimen of that race in the Calaveras Grove, felled while in full vigor of growth at the age of 1240 years. By careful count and measurement I secured a complete record of its growth through the four centuries of its youth and the eight centuries and more of its glorious prime.

Here then was the clue I needed. With those ages and measurements as coördinates, was plotted the curve of growth actually made by that tree throughout its entire life.**

It is No. I of the accompanying chart, and it is to serve as a norm of growth with which we may compare, and thus forecast, the growth of other long-lived trees of kindred stock and similar figure, growing in the same climate and in the same re

1 The measurement for each 200-year period was as follows:
Years
Radius measurement

Years

Radius measurement 200

800

66 inches 400

1000

74 600

I 200

81 The measurements presently to be used in plotting the growth of the junipers are diameter-measurements. This is done merely to facilitate comparison of the different curves by bringing them nearer together, and does not at all affect the conclusions reached concerning the growth of the junipers. Should the diameter of the sequoia be needed, it may, of course, be had by simply doubling these measurements.

** Since the curve is quite regular, it has been possible to continue it in dotted line, with little risk of error, beyond the actual life-time of the tree to the 3000year mark,

The curves of the junipers have been carried out on the same plan.

25 inches
43
56

gion — namely, these junipers. Barring extraordinary accidents, the curve of their growth should be essentially like that of the sequoia, having the same time-scale, and differing only in the scale of magnitude—that is, the ordinates of the juniper curve should at all points be proportional to those of the sequoia curve. The problem is therefore to find the constant ratio between the two.

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Turning now to the first juniper of the above list, we see that the initial point of its curve must of course be at zero of the century scale. A second point is also known, determined by its age of 247 years (at P) and its diameter of 24 inches (Pa). By continuing the vertical coördinate Pa to the sequoia curve at á, we get the ordinate of that curve at the 247-year point Pá, —that is, the radius-measurement of the sequoia at that age, 29.5 P or 0.8 is therefore the ratio sought. Applying this ratio in succession to each of the 200-year measurements of the sequoia growth, we shall have the corresponding measurements of our juniper according to our forecast, which, when plotted, give us curve No. 2 of the chart. In like manner the age and measurements of the Glen Alpine tree result in curve No. 3 of the chart.

The scheme assumes that by the time such a tree as these has reached the age, say of 250 years, it has struck its true pacehas found its proper scale of growth. Forecasting on this basis the “expectation of growth” for these two trees, we find that the mountain juniper might attain the five feet of diameter assigned to its class at about the age of 1300 years, and the valley juniper the seven feet assigned to its class at about 1500. The forecast is probably a little too favorable for the junipers

which occupy exposed positions on the mountain ridges. For the sequoia-record which serves as the basis of the forecast is that of a tree uncommonly well defended from the accidents and stresses which sap the strength and check the growth of middle and later life. Serious damage by fire it seems to have escaped altogether. The deadly freezing and drying winds of winter which the junipers must face singly as they stand scattered about on the storm-beaten heights, could not harm this sequoia deep in its narrow dell and girt about by its giant brethren. So far then as this consideration has weight, it points to a date still later than that just now named for the attainment of its supposed maximum size.

There is also another consideration which seems to point in the same direction. The largest junipers that I have chanced upon have always been found far up on the mountain flanks. Their curve of growth therefore should be represented not by curve No. 2, but by the more pinched and starved No. 3. I feel sure that I have seen among them trees of more than seven feet in diameter, but never having had the wit to measure them, I cannot insist upon that.-Let their maximum be seven feet in diameter. According to curve No. 3 how old should they be? One actually hesitates to name the figure.

On the other hand, the enormous age which used to be claimed for the giant sequoias has been steadily cut down by the increase of definite knowledge, until now it appears that the greatest age demonstrated by actual counts is no more than 2200 or 2300 years. It would seem then that the iper is actually in the race of life alongside of its big brother the sequoia!

May 16, 1917

STUDIES IN THE SIERRA

BY JOHN MUIR

NO. IV. GLACIAL DENUDATION

LACIAL denudation is one of the noblest and simplest

vapor, crystallized into snow, and sown broadcast upon the mountains. Thaw and frost, combined with the pressure of its own weight, change it to ice, which, although in appearance about as hard and inflexible as glass, immediately begins to flow back toward the sea whence it came, and at a rate of motion about equal to that of the hour-hand of a watch.

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This arrangement is illustrated in Fig. 1, wherein a wheel, constructed of water, vapor, snow, and ice, and as irregular in shape as in motion, is being sun-whirled against a mountainside with a mechanical wearing action like that of an ordinary grindstone.

In north Greenland, Nova Zembla, the arctic regions of Southeastern Alaska and Norway, the snow supply and general climatic conditions are such that their glaciers discharge di

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