600 MISCELLANEOUS PAPERS. 



accuracy to ordiuary terrestrial purposes. According to the law of 



gravitatioa 



Mass = Acceleration x (Distance)^ 



and as in tlie case of the earth we can measure the quantities on the 

 right-hand side of that equation with considerable accuracy, we can sat- 

 isfactorily determine the earth's mass in terms of the supposed unit. 

 That suffices for the needs of astronomy, but for other scientific and 

 commercial purposes a standard of mass having a magnitude of about 

 a pound is necessary, and as two such masses can be compared with 

 each other from five to ten thousand times more accurately than either 

 of them can be determined in terms of the supposed unit, three funda- 

 mental units are preferable to two. 



The Chaldeans, Babylonians, Persians, Greeks, and Romans all seem 

 to have had systems of weights and measures based upon tolerably defi- 

 nite standards, but after the decline of the Roman Empire these stand 

 ards seem to have been forgotten, and in the beginning of the sixteenth 

 century the human body had so far become the standard of measure- 

 ment that the units in common use, as for example, the foot, palm, etc., 

 were frequently taken directly from it. The complete table of measures 

 of length was then as follows: The breadth (not the length) of four 

 barley corns make a digit, or finger breadth ; four digits make a pabn 

 (measured across the middle joints of the fingers); four palms are one 

 foot ; a foot and a half is a cubit ; ten palms, or two feet and a half, are 

 a step; two steps, or fiv^e feet, are a pace; ten feet are a perch; one 

 hundred and twenty-five paces are an Italic stadium; eight stadia, or 

 one thousand paces, are an Italic mile ; four Italic miles are a German 

 mile; and five Italic miles are a Swiss mile It was then the practice 

 to furnish standards of length in books by printing in them lines a 

 foot or a palm long, according to the size of the page, and from these 

 and other data it appears that the foot then used on the continent of 

 Europe had a length of about ten English inches. 



In England the first attempts at scientific accuracy in matters of 

 measurement date from the beginning of the seventeenth century, when 

 John Greaves, who must be considered as the earliest of the scientific 

 metrologists, directed attention to the difference between the Roman 

 and English foot by tolerably accurate determinations of the former, 

 and also attempted the investigation of the Roman weights. He was 

 followed by Dr. Edward Bernard, who wrote a treatise on ancient 

 weights and measures about 1G85, and towards the end of the century 

 the measurements of the length of a degree by Picard and J. D. Cassini 

 awakened the attention of the French to the importance of rigorously 

 exact standards. In considering the progress of science with respect 

 to standards of length, we may safely confine our inquiries to the En- 

 glish yard and the French toiseand meter, for during the last two hun- 

 dred years they have been almost the only standards adopted in scien- 

 tific operations. • 



