202 APPENDIX. [No. XII. 



definite conditions of attraction as unity, and by multiplying or sub- 

 multiplying it we obtain aU other measures proportionate to that unit. 

 The Legislature formerly thought fit to take three barleycorns from the 

 middle of the ear, from which they formed a m^easure called an inch. Of 

 coui'se a unit derived from anything so uncertain as three barleycorns is 

 most unsatisfactory, for every measure thus made would doubtless vary. 



" The greatest anxiety has been felt by all nations to find some unit of 

 length to which at any time posterity might be enabled to refer aU future 

 measures, but we have already seen that philosophers have been attempting 

 an impossibility. The French have taken that quadrant of the meridian 

 which passes through Fontenara and Greenwich, the middle of which is in 

 the 45th degree of latitude. This measure they have divided into ten 

 million parts, each part of which they constitute a comparative unit. In 

 assuming this measure, it is perfectly impossible exactly to obtain the 

 greater measure to divide, and even, in fact, we do not know whether the 

 earth, in a series of ages, may not slightly alter in form. The English 

 have assumed the length of the pendulum vibrating seconds in a particular 

 latitude as a unit of measure, but that assumption is highly objectionable, 

 because it infers the existence of something absolute in time, which is not 

 the fact. It, moreover, first requires us to ascertain or determine the 

 duration of a second, which wiU be as difficult for posterity as the determi- 

 nation of a measure for length. The length of the pendulum vibrating 

 seconds appears to vary not only in the same latitude, but even slightly, 

 from some unknown causes, in nearly the same spot ; and, moreover, no 

 two pendulums, of as nearly the same length as human ingenuity can form 

 them, will vibrate in exactly the same time. The best mode of making 

 and maintaining a new standard of measure for this country has lately 

 occupied the attention of the Government and philosophers, in consequence 

 of the former standards having been destroyed by fire in the Houses of 

 Parliament. Although three or four sets of these standards were then 

 made with the utmost human ekill, philosophers cannot determine that 

 these duplicates are exactly similar to those destroyed. This forms an 

 excellent practical proof, not only of the impossibility of possessing an 

 absolute standard, but also the impracticability of using it if we obtained 

 it ; because, as we are unable to weigh below 1-lOOOOth of a grain, so we 

 are incompetent to measure below a certain amount. Probably, in 

 measuring, we can obtain rough results to the 1-lOOOOOOth of an inch ; but 

 as the measures decrease in length, so the errors increase, as all measure- 

 ments must only be regarded as rough comparative approximations to truth. 



"Under these circumstances, we find that our standards are purely 

 arbitrary, and, therefore, the best mode that can be adopted is, to take 

 any arbitrary length, which should be as near the inch now adopted as 

 possible. This measure we should constitute our arbitrary unit, or inch, 

 to which aU other measures should be referred. Several copies, that is, as 

 near as human ingenuity and skill can make copies, should then be formed, 

 and deposited in various places of security for reference. This artificial 

 unit, moreover, should be compared by different observers, and by different 

 instruments, with aU the most fixed things in the material world, so that 

 if, by any accident, the primitive artificial standard was lost, posterity 

 might be enabled to compare their measures with ours; and though, 

 doubtless, they would never be able to obtain the exact relative size of our 



