332 Mr. Lubbock on Cask-Gaging. 



to ascertain : the line has most likely been laid down for a par- 

 ticular value of h. 



The value of q, for the third variety, is found in the same 

 way to be approximately ^ (b — h), and the error of the con- 

 tent would be = — — {b — h} 2 . 



The sliding-rule or head-rod used in gaging affords the 

 means of multiplying the square of the mean diameter by 



4x255-273 ' 

 For gaging by the pen, it would be convenient to have a table 

 of the logarithms of the numbers in Mr. Symons's Table, en- 

 titled " Areas of the Head Diameters," instead of the num- 

 bers themselves. With these, and a table of the logarithms of 

 numbers from 1 to 1000, to four decimal places (both of which 

 might be contained on a single quarto page,) the content of 

 casks might probably be calculated as readily as by means of 

 the sliding-rule. It must be recollected that the principle 

 upon which the line on the head-rod gives the quantity q to 

 be added to the head-diameter is only a rough approxima- 

 tion, which may be out nearly half a gallon, and which stands 

 in need of a subsequent correction. 



The method of determining the ullage of a cask by the line 

 on the head-rod marked S Ly (Symons, p. 214,) is not strictly 

 accurate in principle ; but how far the error which is so intro- 

 duced is sensible in practice, depends upon how far it is de- 

 sirable that the approximation should be carried, and how far 

 the principle itself is modified afterwards by any subsequent 

 correction. The ullage cannot be considered strictly as depend- 

 ent on (or as a function of) the dry inches and the content of the 

 cask as it is by the method alluded to. 



In practice an error in determining the content of a cask 

 may arise either from the errors above noticed, which are in- 

 troduced by calculating the content approximately by the 

 sliding-rule, having given the dimensions and the variety, or 

 from an error in ascertaining the dimensions, or from an er- 

 roneous judgement in deciding upon the variety to which the 

 cask is to be referred. 



An error of a tenth of an inch in all the linear dimensions 

 of a cask will make a difference in a cask holding 1 16 gallons, 

 of about a gallon, which is, perhaps, the maximum of this 

 error. It must be recollected also, that the instruments used 

 in ascertaining the external dimensions are of a nature to 

 stand in need of occasional adjustment, and that the difficulty 

 of ascertaining the internal dimensions is considerable, from 

 the irregularity of the thickness of the staves. The rules and 

 callipers used in gaging are liable to slight but not insensible 



