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Log Scaling On Android Allegro 3

Scribner History

This rule was published in 1846 by J.M. Scribner, a country clergyman.
Let the Author Describe his rule:
"This table has been computed from accurately drawn diagrams for each and every diameter of logs from 12 inches to 44, and the exact width of each board taken after being squared by taking off the wane edge and the contents reckoned up for every log, so that it is mathematically certain that the true contents are here given, and both buyer and seller of logs will unhesitatingly adopt these tables as the standard for all future contracts in the purchase of sawlogs where strict honesty between party and party is taken into account. In these revised computations I have allowed a thicker slab to be taken from the larger class of logs than in the former edition, which accounts for the discrepancy between the results given in these tables and those in former editions."
"The diameter is supposed to be taken at the small end, inside the bark, and in sections of 15 feet, and the fractions of an inch not taken into the measurement. This mode of measurement, which is customary, gives the buyer the advantage of the swell of the log, the gain by sawing it into scantling, or large timber, and the fractional part of an inch in the diameter. Still it must be remembered that logs are never straight and that often times there are concealed defects which must be taken as an offset for the gain above mentioned. It has been my desire to furnish those who deal in lumber of any kind with a set of tables that can implicitly be relied upon for correctness by both buyer and seller, and to do so I have spared no pains nor expense to render them perfect. And it is to be hoped that hereafter these will be preferred to the palpably erroneous tables which have hitherto been in use. If there is any truth in mathematics or dependence to be placed in the estimates given by a diagram, there cannot remain a particle of doubt of the accuracy of the results here given."


Here is a bio from the history of Schoharie County, NY
Here are his grades from Union College.
A classical education actually meant a Classical Eduction

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) provides a facsinating portrait of both Scribner and Doyle.

"It is possible that as a young man [Scribner] working in the woods of his father's Vermont farm he had had personal contact with the inequalities of the existent board-foot measurement. It is also possible that with his insistence on mathematical precision in all things he had been irritated to action by the extravagant claims of the accuracy of the Doyle Rule. His solution of the problem was to draw to scale circles representing the top ends of logs and then to draw within these circles to the same scale rectangles representing the ends of as many boards as might be sawed out of these circles, being careful to maintain a proper allowance for slabs and for the saw cuts between the boards. This was an entirely new approach to the problem of devising a log rule, and it commanded widespread attention."

Scribner's book "Scribner's Ready Reckoner and Log Book, for Ship Builders, Boat Builders and Lumber Merchants," was first published in 1846. Thereafter it went through a number of reprints.

Below is the Cover of the 1866 Edition


Below is the Volume Table from 1866 Edition
Note that the lengths range from 10' to 25' and diameters from 12" to 25". Also, the volumes are expressed in actual Board Feet, not rounded to the nearest 10.


Now here is where the story gets really interesting.
Apparently in the early 1870's Scribner and his publisher, George Fisher, must of had some kind of falling out. At some point in the early 1870s, Fisher was able to purchase the rights to Scribner's book. It also turns out that Fisher also owned the rights to Doyle's own Ready Reckoner book. Perhaps, Fisher was planning to publish a new edition that combined the best of both Scribner's and Doyle's books.
But, that is not what happened. In 1876, Fisher published a new book titled "Scribner's Lumber and Log Book," that was basically the same as the original Scribner book, except that the Scribner Log Volume table was replaced with the Doyle table. It is interesting not note that J.M. Scribner is still listed as the author, with it being advertised as being revised, enlarged, and improved by a Daniel Marsh, Civil Engineer. One could surmise that Marsh convinced Fisher that the Doyle rule was the superior rule.
In the new book, the author (whoever that was), justified the change because the Doyle rule was more accurate and would lead to fewer disputes among buyers and sellers. The new book also changed the way the original Doyle Rule handled rounding. Whereas the original always truncated fractional values down to the nearest board foot, Fisher and Marsh raised them upwards.
It is amusing to see the old Scribner log diagram juxtaposed with the Doyle table that is not a diagram rule at all.


Things get even more confusing with the publication of the 1882 edition.
Fisher and Marsh extended the Doyle rule to handle smaller logs (8' & 9') and also logs with diameters of 8" and 9" inches. The new edition also extended the Doyle rule upwards to handle logs up to 40 feet in length and diameters from 45 to 60 inches.
They introduced a major change when 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."

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."


Henry S. Graves, in his original 1903 edition of his Forest Service publication The Woodsmen's Handbook, Part I, observes that the Doyle rule (as published by Fisher) "... was originally intended that in the use of this rule the average diameter of the log should be taken, but the usual custom is to measure the diameter inside the bark at the small end."

Ultimately, the Doyle table as produced by Fisher has survived to this day, sans the average diameter faux pas.

Henry S. Graves, also in his original 1903 edition of his Forest Service publication The Woodsmen's endorses the use of the original Scribner Table.
Here is the table from Graves' Book. In an important footnote Graves adds that the entries for logs under 12' were supplied by the Santa Clara Timber Company, Santa Clara, NY, and the entries for lengths longer than 25' were supplied the Hurley Brothers, Bay City, MI.
Note that the table is un-rounded. No Decimal C here.


The US Forest Service" According to the Forest History Society:

"A presidential proclamation in 1891, authorized the creation of the Forest Reserves in the United States. The General Land Office administered these lands until 1905, when the forest reserves were transferred to the newly created Forest Service. Gifford Pinchot, chief forester, and the "Use Book Committee" revised earlier regulations and instructions needed to guide the public and the Forest Officers in the use of the National Forest Reserves. Published in 1905 as The Use of the National Forest Reserves, it came to be known as the Use Book. Annual editions of the Use Book were released. From its beginnings as a pocket-sized, 142-page document, the Forest Service manual has grown to encompass multiple volumes, in both print and electronic formats."

Here is the Cover of the 1905 Book:


And here is the paragraph regarding log scaling in the section on Timber Sales:


Did Scribner know Doyle?

If they did not know each other, I would be surprised.
We think that Edward Doyle was born in 1805 and lived in Rochester, New York.
Here is the 1850 Census record for the Doyle family:


We see five members, Edward 45, Catharine 18, Mary 16, Elisabeth 14, and James 12. Apparently, no wife was recorded in the household.
His first "Ready Reckoner" was published in 1825 -- meaning he was just 20 years old when it was published. I would say that was quite an accomplishment.
Edward Doyle appears in the Rochester City Directory in 1827; his occupation listed as merchant, residing on Hughes Street.

Doyle9 Strangely, Doyle does not reappear in the Directory until 1849. As a grocer.

Doyle11 We also know that the editions of Doyle's "Ready Reckoner" were published by a Rochester publisher.
Hoyt & Porter (Rochester) published the 1837 Edition.
Joseph H Jennings (Rochester) published the 1847 Edition.
William Alling (Rochester) published the 1853 Edition.
Indeed, in the preface to the 1847 edition (only one year after Scribner's first edition), Doyle takes a shot at Scribner:


Remarkably, Doyle has recruited the mayor of Rochester to endorse his Volume Table over that of Scribner.
Now here is (I think) the 1850 Census record for the Scribner family:


We see six members, John Sr. 44, Ann 43, John Jr. 10, Margaret 8, Erskine 6, Catharine 0, Arathusa 24, and a Dinah Eckerson 53.
The address is in Middleburgh, NY.
Apparently, Scribner's stay in Rochester was fairly short; he is only listed in the Rochester City directory 1945/46.


His occupation is listed as "Aquaduct." The Aquaduct (as described below) was part of the Erie canal built over the Genesee River. We do not know in what capacity Scriber was employed.


Scribner was a mathematician who published a book on the measurement of volumes for various objects in 1844, prior to his Ready Reckoner. His book was titled: "A PRACTICAL SYSTEM OF MENSURATION OF SUPERFICIES AND SOLIDS".
Here is part of the table of contents:


From this example, it is clear that Scribner was well acquainted with the mathematical tools necessary to address the problem of how much lumber does a tree contain?
It is my thought that Scribner came across Doyle's book while he was in Rochester. Given his passion for geometry and the measurement of solids, he was probably struck by the:


The above is taken from Grave's "The Woodman's Handbook" PUBLISHED IN 1910. I daresay Scribner might have felt the same way.
Here is the problem. Let's say you have a 28" diameter log. You deduct for 4" for slab (twice) and you end up with basically a 20" square, for 400 square inches.
See below:


That looks fine; the 20" square is the largest square that you can fit in a 20" diameter circle.
But as the diameter decreases, the square decreases in size to be much smaller than the largest square that can fit in a circle.
See below for a 16" diameter log.


By deducting 8" from the 16" in diameter, we obtain an 8" square, equalling 64" square inches. But, in reality, the 16" circle could fit a square of 11.3" or about 128 square inches. That is twice the size of the Doyle square.
The reverse is also true. As the diameter increases, the square grows to be larger than would fit in a circle.
See below for a 34" diameter log. The square is 26" x 26" (676 square inches), after deducting the 8" for slab.


But, in a 34" diameter circle, the largest square that will fit is basically 24" x 24", or 576 square inches.
The 4" slab deduction is not enough in this case.
If the goal was to find the largest square that would fit in a circle, the Doyle rule should read (D/√2) * (D/√2) instead of (D-4)*(D-4). The largest square that will fit in any diameter circle is the diameter divided by the square root of 2.

My thought is that Scribner went through the same type of reasoning as above and was intellectually offended.
Scribner then devotes considerable time to develop an alternative method for determining the volume of lumber in logs of various lengths and diameters. As is well known, his method took the practical approach of drawing circles of various diameters and then trying to see how many 1 x 4", 1 x 6", 1 x 8" etc., he could place in the circle, allowing for 1/4" saw kerf.

His preface to his table states his certainty in the approach:

"It has been my desire to furnish those who deal in lumber of any kind with a set of tables that could be implicitly relied upon for correctness by both buyer and seller, and to do so, I have spared no pains nor expense to render them perfect: and it is to be hoped, that hereafter these will be preferred to the palpably erroneous tables which have theretofore been in use. If there be any truth in mathematics, or any dependence to be placed in the estimate given by a diagram, as shown in the preceding drawing, there cannot be a particle of doubt of the acuracy of the results here given."

He might have just replaced the words "palpably erroneous" with Doyle.

Did Scribner know Doyle?

We don't have any evidence that they did. But, there surely were aware of each other's presence in Rochester, New York in the mid 1840's. Back then, Rochester had a population of around 25,000 and a small downtown. If they didn't actually cross paths at some point, I would be mightily surprised.

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