396 PROCEEDINGS OF THE AMERICAN ACADEMY 



Since the investigation of 1882, it has been possible to make the 

 relation between B^''- and the original units more secure through the 

 medium of the yard and meter C. S. In the present discussion it was 

 thought better to vary the method of determining the value of X. 



Let X = the three-inch space beyond the limits of the yard B^'^. 



y = the distance between tlie defining line of this space and the 

 defining line at this end of the meter i?./". 

 Then 



M= r -{-x-^y. 



The value of x was determined by comparing this space with the 

 four three-inch spaces composing the first foot of B"\ This was very 

 easily and expeditiously done by setting the stops of the comparator at 

 a distance approximately equal to x, and then comparing each space 

 with this constant distance. 



For the measurement of the distance y, a space of two inches was 

 laid off upon a short bronze bar with subdivisions to half-inches. The 

 third half-inch is subdivided into five equal parts, and the third sub- 

 division is again subdivided into ten equal parts. The following rela- 

 tions were found between these subdivisions. • 



Half-Inch Spaces. 



July 15. July 17. July 19. July 19. July 20. July 21. July 22. Mean. 2 



I. =: — 4.4div. —2 Idiv. — 2.5diT. -2.8aiv. — 2.8aiv. +0.4aiT — l.Sdiv. — 2.3div. = -1.2(1^ — 1.2|ii 

 II.rr+0.1" +1.8" +3.5" +3.5" +2.9" +0.5" +2.8" +2.1" = +1. V ^O.l^i 



III. = +2.5" +2.2" —2.1" —1.7" —11" —1.3" —1.6" -0.5" := —0.2ft -0.3/it 



IV. =+1.8" —1.9" +1.1" +1.0" +1.0" +0.2" +0.7" +0.6" rr +0.3/^ +0.0fi 



One-Tenth Inch Spaces. 



