258 On Measuring growing Timber. 



and stepping backwards until the reflected image of the point 

 at which the height is wanted coincide with a mark made a 

 few feet above the root of the tree, level with the eye of the 

 observer : the latter height being added to the observer's dis- 

 tance from the centre of the root of the tree, is equal to, or 

 gives, the height wanted. The next operation is to find the 

 diameter at middle height, or at such other point where the 

 most correct average appears to be ; and generally the readiest 

 mode to do this is, for the observer to keep on the same spot 

 where the height was found ; standing at which, let the reflected 

 image of one side of the tree, at the point wanted, be brought to 

 coincide very exactly with its opposite side, as seen by direct vision ; 

 and thus the angle which the diameter subtends will be found; 

 and, by taking the vertical angle to the same point, the data will 

 thus be obtained for finding the diameter, by the rules of 

 trigonometry ; and the diameter being obtained, hence the cir- 

 cumference ; and, finally, the quarter girt, and the measurable 

 height, being also obtained, thence the size of the tree by calcu- 

 lation, or the ordinary tables, or slide rule, or decimal multi- 

 pliers. (For various other modes, see Dr. Olinthus Gregory's 

 Mathemat.for Pract. Men, some of which are very neat.) 



But, as customary measure is not founded upon strict mathe- 

 matical principles, it is unnecessary, in oi'dinary cases, to resort 

 to the strict rules of trigonometry ; and both a ready and 

 sufficiently correct approximation may be made, if the diameter 

 has been taken at, or nearly at, middle height, and the observa- 

 tion made from the point whence the height was ascertained as 

 above described, by adding to the observer's distance from the 

 tree one tenth part thereof, which will give the distance from 

 his eye to the point where the diameter is taken ; and, by multi- 

 plying the distance into the natural tangent of the angle which 

 the diameter subtends, the diameter will be found with sufficient 

 correctness. 



As the diameter of trees, when the observer is at the above 

 distance, seldom exceeds an angle of 5°, the natural tangents for 

 every minute up to 5° can be marked in a memorandum book 

 to the extent of three figures; and, in like manner, the natural 

 secants for every 15' between 15° and 30° might also be marked ; 

 and, by using them as multipliers into the base or observer's 

 distance from the tree, the distance to the point where the dia- 

 meter is taken will be given more correctly than by adding one 

 tenth, as above noticed. 



The following example will make the foregoing description 

 understood:. — A few years ago, having been requested to measure 

 the large larch tree at Dunkeld, the following observations were 

 taken : — The ground being level, upon one side of the tree a 

 small piece of paper was fixed, 5 ft. above its roots ; and, stepping 

 back with the sextant set at 45°, the reflected image of the top 



