THE ART OF WEIGHING AND MEASURING. 615 



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 pre- 

 cisely 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 employed. 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 co-efiicients of expan- 

 sion of each of the substances in the two pans; the temperature of the 

 air, its barometric pressure, and the pressure, both of the aqueous va- 

 por, and of the carbonic anliydride contained in it. 



Judging from the adjustment of the pile 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 one part in 

 ten thousand. 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 that which he and Mr. Bird used in their observa- 

 tions upon the Exchequer weights, for the Parliamentary Committee 

 of 1759, was sufficiently exact "to discern any error in the pound weight 

 to the 230,400th part of the weight."* In 1798 Sir George Shuckburgh 

 had a balance sensitive enough to indicate 0.01 of a grain wiien loaded 

 with 16,000 grains, or about one part in 1,(300,000. The balanc(> used 

 by Fortin in 1799, in adjusting the kilogram of the archives, was not 

 quite so delicate, its sensitiveness being only the one-millionth part of 

 its load; but in 1844, for the adjustment of the present English stand- 

 ard pound, Professor Miller employed a balance whose index moved 

 about 0.01 of an inch for a change of 0.002 of a grain in a load of 7,000 

 grains.t He read the index with a microscope, and found the probable 

 error of a single comparison of two avoirdupois pounds to be one twelve- 

 millionth of either, or about 0.00058 of a grain. At the present time it 

 is claimed that two avoirdupois pounds C£n be compared with an error 

 not exceeding 0.0002 of a grain ; and two kilograms with an error not 

 exceeding 0.02 of a milligram. 



The mean solar day is the natural unit of time for the human race, 

 and it is universally adopted among all civilized nations. Our ulti- 

 mate standard of time is therefore the rotation of the earth upon its 

 axis, and from that rotation we determine the errors of our clocks and 

 watches by astronomical observations. For many purposes it suffices 

 to make these observations upon the sun, but when the utmost precis- 

 ion is desired it is better to make them on the stars. Until the close 



12, p. 456. 1 44, pp. 762 and 943. 



