August 



D» 



889] 



NATURE 



;8i 



while from 122 comparisons made in January, July, and 

 August, 1 84s, 



T = RS - o '00429 grain. 



])y combining these values with the results of the weighings 

 made in 1824-29 — namely, 



S/ = U - 0*52956 grain, 

 RS = U - 0'5244i grain, 



where U designates the lost standard — the comparisons with S/ 

 gave 



T =: U - 0-52851 grain, 



while those with RS gave 



T = U - 0*52870 grain. 



To the first of these expressions double weight was assigned, 

 because the comparisons of T and U with S/ were about twice 

 as numerous as those with RS. The resulting mean was 

 therefore 



T = U - 0-52857 grain = 5759"47I43 grains, 



and from that value of T the new standard avoirdupois pound of 

 7000 grains was con-tructed. 



From some time in the fifteenth century imtil the adoption of 

 the metric system in August 1793, the system of weights em- 

 ployed in France was the poids de viarc, having for its ultimate 

 standard the pile de Charlemagne, which was then kept in the 

 Mint, and is now deposited in the Conservatoire des Arts et 

 Metiers. The table of this weight was 



72 grains = i gros = 72 grains. 

 8 gros = I once = 576 ,, 

 8 onces = i marc = 4608 ,, 

 2 marcs = i livre = 9216 ,, 



The origin of the pile de Charlemagne is not certainly known, 

 but it is thought to have been made by direction of King John 

 (a.d. 1350-64). It consists of a set of brass cup- weights, fitting 

 one within the other, and the whole weighing 50 marcs. The 

 nominal and actual weights of the several pieces are as 

 follows : — 



50 ± O'O 



In determining the relation of the poids de marc to the metric 

 weights, the Committee for the Construction of the Kilogramme 

 regarded the entire / Ic de Charlemagne as a standard of 50 marcs, 

 and considered the individual pieces as subject to the corrections 

 stated. On that basis they found 



I kilogramme — i8,827"i5 French grains ;^ 



and as a kilogramme is equal to 15,432 -34874 English troy grains, 

 we have 



I livre, poids de marc = 7554-22 troy grains. 

 = 489-505 grammes. 



The metric standard of weight, called a kilogramme, was con- 

 structed under the direction of the French Academy of Sciences 

 simultaneously with the metre, the work being done principally 

 by Lefevre-Gineau and Borda. It was intended that the kilo- 

 gramme should have the same mass as a cubic decimetre of pure 

 water at maximum density, and the experimental determination 

 of that mass was made by finding the difference of weight in air 

 and in water of a hollow brass cylinder whose exterior dimensions 

 at a temperature of 17° -6 C. were : height = 2-437672 decimetres, 

 diameter =: 2-428368 decimetres, volume = 1 1 -2900054 cubic 

 decimetres. The difference of weight in question was first 

 measured in terms of certain bra^s weights, by the aid of which 

 the platinum kilogramme of the Archives was subsequently con- 

 stnicted, special care being taken to apply the corrections 

 necessary to reduce all the weighings to what they would 

 have been if made in a vacuum (" Base du Systems Metrique," 

 t. iii. pp. 574-75). 



' " Base du Systeme Mc:rique," t. iii p. 638. 



The best resulls hitherto obtained for the weight of a cubic 

 decimetre of water, expressed in terms of the kilogramme of the 

 Archives, are as follows ^ : — 



These results show the extreme difficulty of determining the 

 exact mass of a given volume of water. The discordance between 

 the different observers amounts to more than one part in a 

 thousand, while good weighings are exact to one part in eight or 

 ten millions. Without doubt two weights can be compared at 

 least a thousand times more accurately than either of them can 

 be reproduced by weighing a specified volume of water, and for 

 that reason the kilogramme, like the English pound, can now 

 be regarded only as an arbitrary standard of which copies must 

 be taken by direct comparison. As already stated, the kilo- 

 gramme is equivalent to 15,432-34874 English troy grains, or 

 about 2 pounds 3 ounces avoirdupois. 



In consequence of the circumstance that the mass of a body is 

 not affected either by temperature or flexure, weighing is an. 

 easier process than measuring ; but in order to obtain precise 

 results many precautions are necessary. Imagine a balance with, 

 a block of wood tied to its right-hand pan and accurately 

 counterpoised by lead weights in its left-hand pan. If, whh 

 things so arranged, the balance were immersed in water, the 

 equilibrium would be instantly destroyed, and to restore it all 

 the weights would have to be removed from the left-hand pan, 

 and some of them would have to be placed in the right-hand 

 pan to overcome the buoyancy of the wood. The atmosphere 

 behaves precisely as the water does, and although its effect is- 

 minute enough to be neglected in ordinary business affairs, it 

 must be taken into account when scientific accuracy is desired. 

 To that end the weighing must either be made in a vacuum, or 

 the difference of the buoyant effect of the air upon the substances- 

 in the two pans must be computed and allowed for. As very 

 few vacuum balances exist, the latter method is usually em- 

 ployed. The data necessary for the computation are the latitude 

 of the place where the weighing is made and its altitude above 

 the sea-level ; the weights, specific gravities, and coefficients of 

 expansion of each of the substances in the two pans ; the 

 temperature of the air, its barometric pressure, and the pressure 

 both of the aqueous vapour and of the carbonic anhydride 

 contained in it. 



Judging from the adjustment of the ///f de Charlemagne, and the 

 Exchequer troy weights of Queen Elizabeth, the accuracy attained 

 in weighing gold and silver at the mints during the fourteenth, 

 fifteenth, and sixteenth centuries must have been about i part 

 in 10,000. The balance which Mr. Harris, of the London Mint,, 

 used in 1743 indicated one-eighth of a grain on a troy pound, or 

 about one part in 50,000; while, according to Sir George Shuck- 

 burgh, the balance used by Messrs. Harris and Bird in making 

 their observations upon the Exchequer weights, apparently in 

 1758 or 1759, turned with 1/230,000 part of its load. In 1798^ 

 Sir George Shuckburgh had a balance sensitive enough to 

 indicate o-oi of a grain when loaded with 16,000 grains, or 

 about one part in l,6oo,coo. The balance used by Fortin in 

 1799, in adjusting the kilogramme of the Archives, was not 

 quite so delicate, its sensitiveness being only the l,ooo,cooth 

 part of its load ; but in 1844, for the adjustment of the present 

 English standard pound. Prof Miller employed a balance whose 

 index moved about o-oi of an inch for a change of o-oc2 of a 

 grain in a load of 7000 grains. He read the index with a micro- 

 scope, and found the probable error of a single comparison of 

 two avoirdupois pounds to be 1/12,000,000 of either, or about 

 0-00058 of a grain. At the present time it is claimed that two 



'Tliis t.-ible has been d;duccd "rom the data given ly Prof. Miller ia 

 Phi', Trans., 1856, p. 760. 



