On the Theory of parallel Lines in Geometry. 42S 



Tliis table exhibits at one view the content for any length 

 of two feet diameter: thus at 40 feet in length stands 125-66 

 feet, which is that found by the first original method by ope- 

 ration; and as all other diameters are treated in the same 

 manner, in my general table, this sufficiently illustrates the 

 whole. 



The factor at the head is a common multiplicator to reduce 

 any length of that diameter to the content. Thus : 



Factor 3-1416 



40 length. 



Feet 125-6640 content, 

 which agrees both with the tabular content at 40 feet length, 

 and also with the content given by the operation. 



The argument, hitJierto so plausible, of " ease and brevity" 

 falls, therefore, at once to the ground ; because neither of the 

 original methods here projiosed requires either the same time 

 or trouble as the girting method. Even the measuring of the 

 log in two frusta requires no more time than to girt; for it is 

 manifest that the taking of a diameter is not a fourth of the 

 trouble of girting and quartering the girt, and then applying 

 the latter to the rule to determine the real dimension ; and in 

 surveying of timber standing, these original methods are not 

 a fourth of the labour of the girting or customar}'^ method. 



As this cannot be viewed as a trivial matter to manj' of your 

 readers, I beg, in conclusion, to make them an offei*, collec- 

 tively and individually, of my personal service to carry this 

 theory into absolute practice ; and as they value their ova\ in- 

 terest, and prefer truth to falsehood, I invite them to join with 

 me in explotling a system which has been so long the theme 

 of just reprobation. 



An Act for the future regulation of weights and measures is 

 l)efore the I^egislature. 



Let the precepts here submitted be recognised in that Act, 

 and I pledge myself, that within six months afterwards I will 

 put it into practice in every part of the nation. 

 I am, gentlemen. 



Your most obedient humble servant, 



William Gutteridge. 



LXXXV. On the Theory of parallel I Aiies in Geometry. By 

 Mr, Henky Mkiklk. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, — JLme theory of parallels is a subject whidi 

 seoins to have iiigogt-d ihc attention of geometers from a period 



