30 MR J. Y. BUCHANAN ON THE 



(6) Let us now consider the preparation of a weight of 1 gram in aluminium for the 

 hydrometer, against a standard gram weight in platinum. We take the specific gravity 

 of aluminium at 2*5 and that of platinum at 21. 



The volume of a gram of platinum is therefore 1/21 cubic centimetre, and it displaces 

 this volume of air, which weighs 0"057 milligram. Therefore the standard platinum 

 gram weighs in air 0*999943 gram or 0*057 milligram less than in vacuo. If w'e are 

 working actually in the vacuum and we equilibrate the platinum gram with a mass of 

 aluminium, both masses exert the same vertical pressure. But when we admit the air 

 the platinum gram loses only 057 milligram of apparent weight, whereas the aluminium 



gram loses — ;:=0"48 milligram of weight, and its vertical pressure in air is only 

 z '0 



0*99952 gram. 



A more useful result is obtained by equilibrating the platinum and aluminium 

 in air. 



J^et the standard gram of platinum be placed on the one pan of the balance, and let 

 a mass of aluminium which in vacuo weighs 1 standard gram be placed on the other 

 pan. The two masses which, in vacuo, would exactly balance each other, now appear 

 to have different weights. By immersion in the air the platinum gram has lost 0*057 

 milligram and the aluminium gram has lost 0*48 milligram. Let aluminium be 

 added to the aluminium weight until the balance shows equilibrium. The amount so 

 added weighs in air 0*423 milligram. The vertical pressures exerted in the air by the 

 masses of platinum and aluminium respectively are then equal. But this pressure is 

 still short of the standard pressure of 1 gram by 0*057 milligram. Let this weight 

 of aluminium be added to the mass of aluminium already on the pan. When this 

 addition has been made, the total mass of aluminium will exert in air, weighing 1 '2 

 milligram per cubic centimetre, a vertical pressure of 1 gram true. No account has been 

 taken of the buoyancy of the last two additions to the mass of aluminium, because its 

 effect is insensible on our balance. 



In practice the aluminium weights used in any experiment never exceed 1 gram 

 by more than one or two tenths ; therefore, if they have been simply balanced 

 against the corresponding platinum weights in air, the deduction for buoyancy 

 is insensible ; and we have seen that, if the brass weights have been prepared 

 against brass standards in air, the deduction for buoyancy is at the rate of 0*14 milli- 

 gram per gram when 1 cubic centimetre of air weighs 1*2 milligram per cubic 

 centimetre. 



§ 12. Exposed Stem. — Let us consider the effect on the resulting value of the specific 

 gravity of a liquid when the correction for the buoyancy of the exposed stem is 

 applied or is neglected. The effect of buoyancy will evidently be the greater, the 

 greater the length of the exposed stem. Let us take the case of the hydrometer 

 suitably loaded, floating at mm., or the lowest division on the stem, both in the 

 distilled water and m the solution. The volume of the exposed stem is 1*25 cubic 



