MENSURATION IN FRANCE . 687 



siders it equivalent to a cylinder of the same length and a diameter 

 equal to the diameter of the log at its middle point : 



V = -D^L = .7854 D^L = .0796 C^L. 

 4 



Computations are avoided by the use of tables which are very com- 

 monly based on middle circumference instead of diameter. The bark 

 is usually included in the volume unless the log has been peeled. To dis- 

 tinguish the true volume thus approximately obtained from some of the 

 results later to be described, the words "au reel" are generally appended. 



The error of applying this method to long logs is of course recognized, 

 and it is compensated in commercial transactions by modifications in the 

 price paid per cubic meter. 



There are, although no equivalent of this term is current, three "log 

 rules" in common use. They are called "cubage au quart sans deduc- 

 tion," "cubage au sixieme deduit," and "cubage au cinquieme deduit." 

 That they are in truth log rules is evident from their purpose, which 

 is to give the volume of the sawed product of the logs. They are rules 

 of the formula type and are one and all based on entirely erroneous 

 mathematical principles. The formulae are mere rules of thumb. They 

 are: 



Method Formula 



Au quart V= (-) -L= .0625 c-L= .6168 D=L. 



f-\ 

 Sixieme deduit "^ ^^ i ^ J ^"^ ^^ -0434 ^^L = .4284 D^L. 



Cinquieme deduit ^ ^^ ( A l^L^ .04 c-L= .3948 D^L, 



where V = volume in cubic meters, C = circumference, D = diameter, 

 L = length, all in meters. The three forms of each formula show its 

 origin, its simplest form based on circumference, and the same based on 

 diameter. The "au quart" formula will be recognized as our "quarter- 

 girth" rule, and the other two are merely more conservative expressions 

 of the same type. The "au quart" formula actually gives the volume of 

 a square timber cut from the log, but which will be slightly waney- 

 edged at and above its middle point, the point of measurement; the 

 "sixieme deduit" that of a similar stick without wane, but wath sappy 

 edges, while the "cinquieme deduit" gives that of a stick with neither 



