Taylor.] 360 [Oct. 21, 



(Article " Arithmetic"), it is stated in reference to this subject, tliat Fatlier 

 Bouvet, wlio first sugge.sted tliis explanation and communicated it to Leib- 

 nitz, afterward procured, during his residence in China, the Great Fi(jiir& of 

 Fold, which extends as far as Gi. The exact coincidences which he still 

 found to prevail between the combinations of these lines and the figures of 

 the binary notation, left no doubt with regard to the justness of his conjec- 

 ture ; and we cannot help remarking that the restitution of the true sense of 

 those characters, after so long an interval of time, is a very singular fact in 

 the history of science. 



Note C. 



It is interesting to trace the history of the gradual development, in modern 

 times, of the grand but difficult project of obtaining from nature a constant 

 and universal standard of length. It is obvious that no such objects of ulti- 

 mate reference as the human foot, or arm, or cubit, or as "thirty-six barley 

 corns round and dry," can be regarded as natural standards, since they are 

 wholly useless for tlie purpose of any precise determination. And all meas- 

 ures derived from them are purely arbitrary, as their authority is obtained 

 from positive enactment, merely, and not from any agi-eement with their 

 nominal originals. Hence it is not at all surprising that "cubits" and "feet" 

 come to signify anything the civil power may enact ; the former of these 

 denominations ranging through every gradation of value, from the covid of 

 Wy^ inches to the royal Egyptian cnhit of 253^ inches, and the latter from the 

 Pythic foot of 9% inches, to the Geneva foot of 19 inches. Nor would it 

 ever be possible from such sources, to reproduce a lost standard, with even 

 the rudest approach to exactness. As Mr. Adams has well remarked, "For 

 all the uses of weights and measures in their ordinary application to agricul- 

 ture, traffic, and the mechanic arts, it is perfectly immaterial what the natural 

 standard to which they are referable may be. The foot of Hercules, the arm 

 of Henry the First, or the barley-corn is as sufficient for the purpose as the 

 pendulum, or the quadrant of the meridian" {Report to Congress). 



" The first attempt at fixing such a standard as should be accurate and 

 universal, both as to place and time, is due to the inventive genius of the 

 celebrated Iluyghens. That philosopher demonstrated that the times of the 

 vibrations of pendulums depend on their length only. ® * •■■ Hence he con- 

 ceived that the pendulum might afford a standard or unit for measures of 

 length " {Edinburgh Eeview, Vol. ix, page 373). It was in his " Horologium 

 Oscillatorium" (published about 1G70), that Iluyghens proposed the use of 

 the seconds' pendulum as a universal and perpetual measure ; this length to 

 be divided into three equal parts ; and this third part (about 13 inches) to be 

 called the horary foot. 



The celebrated Picard, who first measured from Paris to Amiens in 1669, 

 an arc of the meridian in France, making the degree equal to 68.94.5 miles (a 

 measurement memorable as having furnished Newton with the means of 

 verifying his grand theory, incapable of determination from the pre-existing 

 data), also proposed in 1671, in agreement with the idea of Iluyghens, that 

 the pendulum beating seconds should be adopted as the unit of length. 

 Picard has the merit of having first thrown out the suggestion that the diur- 

 nal rotation of the earth ought to affect the oscillation of the pendulum, and 



