4-20 On lite Mcasuitmnit of TiiitOcr. 



effect, is just the same us the foregoing precept; but tlie ope- 

 ration upon the slicling-iiile is so simple, that the most iUiterate 

 feller of timber can ])erlbrm it just as well as the most expert 

 mathematician ; and I am free to confess, that no other me- 

 thod has yet been proposed, as a substitute, by any means so 

 brief; though an approximation given by Mr. Bonnycastle, to 

 find the content of a cylinder, is certainly very simple. He 

 asserts, that " it is as easy in practice as the false method ;" 

 but, as regards the sliding-rule in the hands of illiterate me- 

 chanics, it certainly is not so. 



The method he proposes is, to multiply a fifth part of the 

 jv.iddle girt squared into twice the length of the log; and as 

 tiii.s would give the content of a cylinder of the same length 

 and of the same diameter as that in the middle, or at die half 

 length, I intend to offer two practical and simple methods, 

 which sliidl effect the object which he contemplated ; and, at 

 the same time that it secures to the grower in any case above 

 20 j^er centum nearer to the value of his property, still leaves 

 an ample excess of quantity to compensate for irregularities ot 

 growth to the purchaser ; because the real quantity, as the 

 frustum of a cone, v/ill ever be in excess of the quantity result- 

 ing from the diameter in the middle, taken as a mean for a 

 cylinder, as will plainly appear from die following : 



Suppose the foregoing figure to represent a log of round 

 timber of 40 feet in length. 



The greater diameter at a = 3 feet ; 



The middle diameter at c — 2 feet ; and 



The least diameter at c= I foot. 



The content of such a log is truly 1 36 feet, and 1 36 thou- 

 sands of another foot; see the following computation, viz. 



3x1X3 = 9 = tripled product of extreme diameters. 



3 — 1 = 2-= 4 = squared difference of those diameters. 



Sum =13^ X -7854 x tP = 136-136 feet. 

 Now, if this log be measured by the present customary me- 

 thod, one-fourth of the girt at c is =1*5708, which squared is 

 2-4'674-, which multiplied into the length (40 feet) gives 98*7 

 feet very nearly ; and if we take 



98*7 feet (the customary content) from 

 136"136 feet (the real content), there remain 

 37*436 feet (the loss sustained by the grower) which is 

 almost 27^ per centum. ! But 



