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This rule was published in 1825 by Edward Doyle.

I haven't been able to locate of copy of this edition, but here is the picture from the second edition published in 1837

And here is a look at the Doyle table.

Doyle's table shows volume entries for logs 10' to 25', with diameters 12" to 36".
Doyle does not specify how he created the table, although it is pretty clear that he used what is the same formula still used today.

The formula is:

BF = ((DIAM - 4)^{2}/16) * LEN

Harold C. Belyea of
the State University of New York, College of Forestry, Syracuse in his article "A Postscript on the Lost Identity of Doyle and Scribner" (1953)
is sceptical that Doyle came up with the rule on his own: "I doubt
that it was he who devised the formula
statement as reported by
Henry S. Graves in his account of
the early history of log rules in the
earlier editions of his *Forest Mensuration*".
Belyea goes on to speculate that:

"In its origin it seems to have been more or less a rule by thumb invented to meet the requirements
of average-sized logs which at that time ran 20 to 30 inehes top d.i.b. It is not known whether Doyle arrived
at his conclusion by observing that 24-inch 16-foot 1ogs usually sawed out about 400 board feet,
and that 4 subtracted from 24 and then multiplied by half of itself, and the product by the length in
feet, and the result divided hy gave 400, and then applied the same, technique to all other diameters
and lengths. Had he been mathematically trained, he would have at once seen that all this
hocus pocus really amounted to squaring and he would have quickly given it to us in its [modern form above]."

Belyea provides no basis for he speculation. I, for one, do not agree with Belyea's speculation.
The simple observation that out of the 400 table entries, only 18 (4.5%) diverge from the formula by more than one board foot, and only 6 diverge by 2 (1.5) or more board feet makes it almost certain Doyle used the formula above.
Given that all his calculations had to be performed by hand and then the table had to be typeset and proofed, I think he did a pretty good job. We will never know if Doyle actually devised the formula but odds are he was aware of it and applied it to generate his table. An alternative explanation is that he may not have wanted to make public the formula in fear that others could easily copy it and make up a competing set of tables.

As noted in the Scribner history page, Scribner's publisher (G.W. Fisher) in the late 1876 published a new edition of Scribner's Ready Reckoner, renaming it Scribner's Lumber and Log Book. Fisher had obtained the copyrights to both Doyle's and Scribner's work and proceeded to replace the Scriber volume table with the Doyle volume table all the while keeping Scribner's name in the title and it's author. Aside from this change, most of the rest of the book is the same as Scribner's last Ready Reckoner.

Here is the title page from the 1882 edition (Apparently there is only one copy of the 1876 edition still around in the University of Rochester Library) along with the preface to the replacement Doyle table. Fisher, and his sidekick Daniel Marsh, decided that the original table created dissension among log buyers and sellers. See their explanation in yellow.

Here is the actual volume table from the original edition published in 1876. The source of this table is NOT the actual original book, but from a reprint published by William Bryce of London, Ontario in 1881. The Bryce version of book was in demand as Ontario had adopted the Doyle (replacing the Scribner rule) in 1879. This is my deduction based on the fact that in 1881, the 1882 edition had not been published -- meaning the table must be from the original 1876 edition.

The table extended to diameters from 25" to 50". Some of the table entries will also changed from the prior Doyle table. The changes corrected some calculations, corrected some rounding, and introduced a few new errors on their own.

Here is the Log Table from the 1882 Edition of Scribner's Log and Lumber Book.

The table further extended to diameters from 50" to 60", and the lengths from 36' to 40'. Again, Some of the table entries will also changed from the prior Doyle table. The changes corrected some calculations, corrected some rounding, and introduced a few new errors on their own.

Fisher and Marsh also went rogue in the 1882 edition.

They introduced a major change in that they substituted the diameter
measurement to be the **average** of the top and butt diameters, rather than that of the **small**
diameter as originally intended by Doyle. In their introduction of the table they say:

"It is customary in measuring logs to take the diameter in the middle of the log
inside the bark. This is obtained by taking the diameter at each end of the log.
adding them together and dividing by 2."

I am sure they did not endear themselves with scalers who now would have to make two diameter measurements than just one. THat said, the change would probably improve the accuracy of the rule.

They also introduced a bark allowance of 1/10 to 1/12 part of the circumference.
As H C. Belyea notes:

"The 1/10 to 1/12 of the circumference is an impossible
allowance for bark and that, if carried out as stated, the scaler would
end up with a smaller diameter than if he had taken the top diameter
inside the bark as originally suggested by Doyle, and as is the
common custom with this rule at the present time."

The Doyle Rule is not popular among academic foresters:

H. C. Belyea in his 1931 book "Forest Measurement" opines that the Doyle Rule is "...probably the least accurate lor rule in common use."

Graves and Zieglar in their 1910 book "A Woodman's Handbook" are "astonished that such a defective rule should have so general use:"

**So why is the Doyle rule still in wide use?**

Chapman (1925) explains:

The rule is used almost to the exclusion of all other rules for hardwoods in parts of the Ohio Valley, and for Southern yellow pine. Its use is extensive in every eastern state outside of New England and Minnesota. In the West, it is not used to any extent.

The Doyle rule reverses the error of the Baxter rule by deducting too large a per cent for slabbing and not enough for sawdust. The wide use of the rule has caused losses of millions of dollars to owners selling logs and standing timber, by improper and defective measurement of contents. The prevalence of its use is due first to the **simplicity** of its application as a rule of thumb. The rule reads: Deduct 4 inches from the diameter of the log as an allowance for slab. Square one-quarter of the remainder and multiply the result by the length of the log. The result is the contents in board feet. Timber cruisers estimate logs in 16-foot lengths. For this length of log the rule would read: Deduct 4 inches from the diameter of the log inside bark, and square the remainder. The result is the contents of the log in board feet, by the Doyle rule. A rule as easily applied as this was sure to be popular.

The second reason for its wide use was its **substitution for the old Scribner rule in Scribner's Log and Lumber Book**, after this publication had already attained a large circulation. As this book was widely accepted as a standard and almost the only publication of log rules, the impetus given to the use of this inaccurate rule by this substitution was tremendous.

The third reason for the continued use of the Doyle rule is the same which operates to prevent reform in the use of log rules in general. **Custom**, or habit of using it, is fixed. So far has this gone that the States of Arkansas, Florida, and Mississippi prescribe its use by statute. Added to this fact that a rule favoring the buyer will be advocated by this class to its own advantage.

One author that lays out a more positive case for the Doyle Rule is Matthew Fonseca in his book "The Measurement of Roundwood" (2005). He suggests that the Doyle Rule, by understating the board footage of small diameter logs serves to compensate for the fact that such logs are less desirable for sawmills because of their lower valued end products and/or higher production costs.

"The rule has been widely criticized as being very inaccurate in predicting product output. While it is true that this rule does a poor job of predicting product output (it grossly understates the relative recoverable product volume of small logs and even medium-sized logs to larger logs), it is not a bad rule for measuring value (especially for logs 9" and larger). Doyle is seldom used for logs under 8" on the small-end. Doyle understates typical lumber recovery by diameter class at a relative ratio to value by diameter class, which often allows a log purchaser to pay a single price per mbf (1,000 board feet), as opposed to having different price levels by size classes. This

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