1887.] «jOJ- [Taylor. 



their almost constant recurrence among different nations, and the close 

 approximation in length of such as have, like the foot, more nearly' ac- 

 quired tiie cliaracter of arbitrary measuree, alike establish the fact tiiat in 

 its origin, measurement of length was by the application of parts of the 

 human body. In some parts of the East the Arabs, it is said, still mea- 

 sure the cubits of their cloth by the forearm, with the addition of the 

 breadth of the otlier hand, which makes the end of the measure ; and the 

 width of the thumb was in like manner formerly added at the end of the 

 yard by the English clothiers. Tlie advantages of such measures for pop- 

 ular use are that they are known by observation and readily understood, 

 and in an average way always capable of being recovered, when more 

 arbitrary standards might be wholly lost. But their great disadvantage is 

 extreme variableness, especial!}'- when directly applied ; and in the grad- 

 ual progress of men's minds toward exactness of conception and reason- 

 ing, three successive plans of insuring greater accuracy have been devised, 

 and two at least have secured permanent adoption. 



The first is that of obtaining a uniform standard by exchanging the 

 measures by parts of the body for conventional or arbitrary lengths, which 

 should represent the average, and which were to be established by law. 



The second plan is that of making accurate comparisons of the various 

 standards of each given sort in a country. Attempts of this kind appear 

 in England to have been commenced under the auspices of the royal 

 society in 1730 and 1742 ; in the former year by a comparison of the En- 

 glish, French and old Koman standards ; and in the latter by the deter- 

 mination (by George Graham) of the length of a pendulum beating sec- 

 onds at London, to be equal to 39.1393 inches, and the construction of a 

 standard j'ard. Of this, under the direction of the House of Commons, 

 Mr. Bird (a celebrated optician) prepared two accurate copies, respectively 

 marked "standard yard 1758" and " 1760," and intended for adoption as 

 the legal standards. He determined and prepared also the pound troy, the 

 original of that now in use. Of these two standards, no intentional alter- 

 ation has since been made ; so that these or their derivatives are now in 

 use in England and the United States. 



The third proposed step toward rendering measures exact has reference 

 rather to the means of making the standards recoverable in case they 

 should be lost. In the definite pursuit of this purpose the French philos- 

 ophers of the time of the Revolution took the lead, and devised the metric 

 system, in which the unit of length is derived from the dimensions of tlie 

 earth, and the units of capacity and weight are made dependent upon the 

 former, while the whole has decimal multiples and subdivisions. The 

 celebrated commission concentred within itself the physical and mathe- 

 matical science of France, but there was one science unfortunately not 

 there represented ; the science of human nature. Looked at from a purely 

 aritlimetical standpoint, the problem of measures suggested but one solu- 

 tion, tliat of the decimal digits. Abstract mathematics could furnish no 

 inducements to binary or octonary divisions or progressions. 



