Some Observatiotis on the Mode of Measuring Timber, 89 



wMch will ever continue to baffle our inquiries. This, however, need 

 not prevent us from making approximations to what must be the 

 truth ; and common sense tells us that the nearer we can make the 

 approximation, without causing practical inconvenience from long- 

 arrays of figures, the better of course it will be. 



Various such approximations have been made by mathematicians, 

 Van Culen estimated that the area of a circle was equal to •7854 of 

 the square of its diameter. Metius, with smaller figures, reckoned it at 

 fll of the same degree. But the proportion which of all others seems 

 (to myself at any rate) to steer the middle way between truth and 

 convenience is that given by no less ancient a personage than Archi- 

 medes, who estimated that \^ of the square of the diameter would 

 give the area of any circle. 



All these are instances of deducing the area of a circle from our 

 knowledge of its diameter. We may also deduce it from our know- 

 ledge of its circumference. "07958 of the square of the circumference 

 will, the mathematicians tell us, give its area. 



Or we may, after the fashion in use, endeavour to discover the area 

 of the circular end by squaring the circle in another manner, by 

 finding the side of a square which shall nearly be equal to the circle ; 

 and so we shall be able to deal with the rounded tree as if it were a 

 squared piece of timber. But here be pleased to note the proportions 

 of' such a side to the circumference, as used for practical purposes, 

 and as stated by the mathematicians. We assume for practical 

 purposes that one quarter of the circumference is equal to the side 

 of such a square; that is to say, 25 per cent, of the inches which 

 make its extent, or -2500. But the proportion given by the mathe- 

 maticians is considerably different. The proportion which such a 

 side bears to the circumference is, they say, larger than -2500 ; for it 

 is -2821, or 28'21 per cent, of the inches of the circumference, or 

 longer by 12'84 per cent, of inches than we usually make it. We 

 see, therefore, at the very beginning that we start with a considerable 

 error ; and consequently, when we square the side to give the area of 

 the end or place where it is taken, we multiply the error also ; we 

 magnify it again when we have to multiply the result by the length 

 to give the contents ; and when we have to add together some hun- 

 dreds or thousands of trees measured in this manner, the error 

 becomes very considerable indeed. 



Suppose, by way of example, that we take the girth of a piece 

 of oak timber as 100 inches ; then the side of a square nearly 

 equal to the circle will, according to the method now in use, be one 

 quarter of this extent, or 25 inches ; and consequently the area given 

 by a square with a side of these dimensions will be G25 square inches. 

 But according to the more exact method of which we have been 



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