Taylor.] ^''O [Oct. 21, 



the equator been the standard chosen, inasmuch as it has no such natural 

 measure, the sextant of it might just as properly have been made the 

 starting unit as its quadrant. And this would have escaped the principal dif- 

 ficulty ; for the sextant will easily supply us with a multiple of the quadrant, 

 though the latter may not conversely so readily commensurate the former. ■ 

 Instructed by such distinguished failures, let us then start with the sex- 

 tant of the equator as our prime unit of measure. We shall thus be able 

 to select a final modulus or rule, mainly with reference to its most desira- 

 ble length — no longer trammeled by the compounding of binary and ter- 

 nary divisions. Ten million metres made the quadrant. Our octonary 

 scale is also furnished with its grand unit (the eighth power of the octade), 

 which for want of a better name we have christened unJcaly (L,0000,- 

 0000)- The sextant of the equator is 21,911199i feet, or 262,934893 

 inches. This divided octavally into unkaly parts, gives us the quotient, 

 15| inches, almost exactly our ideal measure! Midway between the two 

 great rival standards of olden time, the cubit and the foot, it seems the 

 very compromise of differences, the harmonizer of conflicting systems, 

 and supplies us with a "module" perfectly suited to every requirement of 

 popular mensuration. It needs but the application of octonary multiples 

 to complete a metrology simple and unexceptionable. 



Before giving the table, however, it will be proper to suggest a slight 

 modification in the divisions of the circle, as a subject controlling, to some 

 extent, the details of our linear measures. Should the degree retain its 

 present value as the 360th part of the circle, we should advocate strongly 

 the employment of this unit of the equatorial circle, as the origin of our 

 new standard of measure. Dividing the degree into undersell parts 

 CLOO 0000). ■"'G should have a module about one inch longer than that 

 previously obtained, and somewhat nearer, therefore, to the ancient cubit. 

 Its exact length would be 16.717 inches. 



The number 60, however, approaches so near to the octonary under 

 (64) that the temptation would be very strong to reduce degrees, minutes 

 and seconds to the simplicity of the general notation, unless there ap- 

 peared some strong reason for retaining the present sexagenary scale. But 

 there is no special occasion for dividing small arcs into thirds or sixths, 

 that gives this ancient and venerable system any advantage comparable 

 to that we should have of adding up or subtracting degrees, minutes and 

 seconds by a single operation, instead of resorting as now to reduction. 

 On the contrary, the need of frequent binal division is here, as with other 

 values, very apparent ; and in this respect the number 60 is very defec- 

 tive, as it permits but two bisections. The mariners' compass affords us a 

 good illustration of the convenience experienced in a continued bisection 

 of angles.* There would therefore be a positive benefit in substituting 



* The cardinal points dividing the circle into quarters— each quadrant is divided into 

 halves or octants, each octant into halves and quarters called "rhumbs" or "points" 

 (8 in the quadrant), and finally each of these points into halves and quarters ; the rhumb 

 or point being 11° 15', and the quarter rhumb or point 2° 48' 45". 



