Report concerning the new Metrical Sjjlan. . ~ 367 



There was a communication between the external air and the infide of the cylinder, by 

 means of a tube, which ferved to fufpenJ it ; and the weights being of the fime material, 

 the refult in air was the fame as it would have been in vacuo. 



In order* to avoid all dependence upon the relative lengths of the arms of the beam, the 

 weighing was always performed in one and the fame fcale, the thing itfelf being firil coun- 

 terpoifed, and afterwards taken out, in order to admit the equivalent weight in the fame 

 fcale. By 53 experiments, the weight of the cylinder proved to be at a mean 1 1,4660055 of 

 the arbitrary unities, and the extreme difFei^ence among thefe experiments did not amount to 

 45 millionth parts of the unity. The more difficult operation of weighing the cylinder in 

 water was repeated thirty-fix times, and the mean apparent refidual weight proved 0,1094190 

 unities with no greater abfolute difference between the extremes than before. 



The reporter enumerates the various corredlions to which this apparent weight muft be 

 fubjeiled. In the firft place he obferves, that the air fupports the counterpoife ; and does 

 notfupport the body plunged in the water. Secondly, the apparent weight expreflesnot only 

 that of the cylinder, but likewife of the air contained in its cavity. Thirdly, regard muft be 

 had to the denfity of the water, as governed by its temperature. The experiments were 

 made by furrounding the veffel that contained tlie water with pounded ice, which kept the 

 temperature of the water itfelf at three tenths of a degree of the centigrade thermometer 

 above the freezing point ; but the refults were reduced to the maximum of denfity of water, 

 which by another courfe of experiments was found to be at the fourth centigrade degree, con- 

 formably to the experiments of Deluc. Laftly, it was requifite to allow for the expanfion 

 or contradion of the brafs cylinder, by the difference of temperature at the time of admea- 

 furement, and the fubfequent experiment. 



After all redudions, it was found that 11,2796203 cubic decimetres of water at its maxi- 

 mum of denfity weighed 1 1,27, and that one fingle cubic decimetre of water at its maximum 

 of denfity weighs 0,9992072 of the unity, which is the true kilogramme of the new metrical 

 fyftem. 



It remained then to determine the relation between the arbitrary unity made ufe of, and 

 the ancient French weights. For this purpofe the ancient pile weighing fifty marcs, called 

 the pile of Charlemagne, was examined. The whole pile repeatedly weighed was found to 

 be equal to 12,2279475 : whence it follows, that each unity is equal to 18842,9088 grains 

 poids de marc, and that the true kilogramme, or weight, of one cubic decimetre of diftilled 

 water, taken at its maximum of denfity and weight in vacuo, that is to fay, the unity of 

 weight, is 18827,15 grains. The reporter adds in a note, that according to thefe experi- 

 ments, the foot cubic (French) of diftilled water, taken at its maximum of denfity, is 70 

 pounds 223 grains ; and at the temperature of three tenths «f a degree, it weighs 70 pounds 

 141 grains ; and at the temperature of melting iCe it weighs 70 pounds 136 grains. 



The pile of Charlemaine, though very accurately made for the workmanfliip of the four- 

 teenth century, at which time it is pretended that it was made, or renewed, is not accurately 

 the fame in all its parts. The mark taken as the fiftieth part of the whole pile proved to 



3 B 2 be 



