Nov. 20, 1873J 



NA TURE 



49 



nished by o'oooi32, they may be used for the reductions 



of weighings at Paris. 



The values of the pressure of vapour at the same 

 temperatures in millimetres of mercury at o^, according to 

 Regnaiilt's observations, are stated by Prof Miller in a 

 separate Table II. These values are given on the assump- 

 tion that the pressure of va[jour in rooms that are not 

 heated artificially is two-thirds of the maximum pressure 

 of vapour due to the temperature, as shown by the 

 results of experiments on the authority of Biot, Regnault, 

 and Bianchi. 



The actual mode of ascertaining the weight of air dis- 

 placed by two standard weights may now be described. 

 For determining the temperature of the air and of the 

 two standard weights during the weighings, two standard 

 thermometers are placed in' the balance case, and their 

 readings noted at the beginning and end of the weighings. 

 The weight of air displaced by each of two standard 

 weights is to be ascertained by the following formula : 



Log weight in grains of air displaced by P = log. /; + 

 log. A/ + log. (I + eYt) -f log. weight of P in grains - 

 log. AP. 



Here t denotes the temperature of the air by the 

 Centigrade thermometer ; 



b the barometric pressure of the air in millimetres of 

 mercury at 0° C. ; 



'<• the maximum pressure of aqueous vapour contained 

 in the air, also in millimetres of mercury ; 

 /i =. b — 0-378 X j} t' ; 



At the ratio of density of air at i" to the maximum 

 density of water ; 



(•P/ the allowance for expansion in volume of P, or the 

 ratio of its density at o' to its density at t ; 



AP the ratio of density of P at 0° to the maximum 

 density of water. 



By this formula, the required result is to be obtained. 

 The logarithms of the three first terms may be found 

 in Prof Miller's tables, pp. 785-791 of his account of 

 the construction of the new standard pound, Phil. 

 Trans., part iii. of 1S56. 



Reference has already been made to the mode of 

 ascertaining the volume or density of a standard 

 •weight by determining the difference of its weight in air 

 and in water. The following practice for all such hydro- 

 static weighings was adopted by Prof Miller when deter- 

 mining the densities of all the standard weights con- 

 structed under the sanction of the Commission for 

 restoring the Imperial Standards, and is also followed in 

 the Standards Department. In this process it is requisite 

 to employ pure distilled water, and with this object the 

 water used in the Standards Department is twice distilled 

 in a still of the best construction, erected in the office, and 

 the best chemical tests are employed for ascertaining that 

 the water is free from any foreign substances. 



The vessel for containing the distilled water is a glass 

 jar, rather more than 6 inches in internal height and 

 diameter. A stout copper v/ire is stretched across the 

 mouth of the jar (see Fig. 18) in such a manner as to 

 leave a circular space in the middle, large enough to 

 admit the passage of the standard weight P, the density 

 of which is to be ascertained. This copper wire supports 

 two thermometers, adjustable as to their height, for deter- 

 mining the temperature of the water at the mean height 

 of B during the weighings. It also serves to sustain a 

 glass tube, open at both ends, and placed close to the 

 side of the jar. A small glass funnel is inserted in the 

 upper part of the tube, and in the lower part are one or 

 two pieces of clean sponge. 



The standard weight P is suspended from a hook under 

 the right pan of the balance, specially constructed for 

 hydrostatic weighings. A fine copper wire, the weight of 

 which per inch is known, is attached to the hook by a 

 loop, and has another loop at the other end. To this 

 lower loop is attached a stout wire, bent and terminating 



in a double hook, which fits round P, and holds it securely. 

 The counterpoise of P is next placed in the left pan of the 

 balance. The glass jar is placed under the right pan of 

 the balance, P being suspended in it, and the water is 

 gently poured into the funnel and the jar filled to the 

 requisite height above P. The bubbles of air are arrested 

 by the pieces of sponge, and, ascending up the glass tube, 

 are thus prevented from entering the jar. It is of import- 

 ance to ascertain that no bubble of air is attached to P, 

 and if so, it may generally be removed by the feather of a 

 quill. But it sometimes happens that the weight P has 

 an irregular surface, and air attaching to it cannot be thus 

 dislodged. In such cases a small bell-shaped glass jar 

 just large enough to hold P and its supporting wire, is 

 used. This vessel is filled with water sufficient to cover 

 P, and is suspended over the flame of a spirit lamp by a 

 stout wire, bent at its lower end into a ring, into which 

 the jar descends to its rim, and the water is allowed to 

 boil until it is seen that the air has been entirely expelled. 

 When cooled, the small jar containing P is immersed iu 

 the water, which nearly fills the large jar, and the small 

 jar, with its wire, is then disengaged and lowered till P 

 hangs clear of it, when it is removed. The transfer of P 

 from the small to the large jar is thus effected without 

 taking it out of the water. 



For the actual weighing of P in water, after it has been 

 counterpoised in air, weights equal to the difference of 

 weight of P in water and in air, are placed in the right 

 pan till equilibrium is produced, when the readings of the 

 scale are observed. P is next removed, leaving its hook 

 suspended in the water, and a volume of water equal to 

 the volume of P is added to the water in the jar, so as to 

 leave the same quantity of wire immersed as before. The 

 requisite weights are then added to the right pan, until 

 the equilibrium, which has been disturbed by the removal 

 of P, is again produced, when the reading of the scale is 

 observed and noted. This gives the actual weight in 

 water of P. 



The thermometers in the water are so placed as to give 

 the temperature of the water at the centre of gravity of 

 P. Another thermometer is placed in the balance case 

 to give the temperature of the air during the weighings. 

 The reading of the barometer is also noted. 



Having determined the weight of P in air of ascer- 

 tained density, its volume and density are calculated 

 according to the following formula, the unit of volume 

 being the volume of a grain weight of water at its maxi- 

 mum density : — 



Let P in water at i" appear to weigh as much as O in 

 air. Then the weight of water at t" displaced by P = 

 weight of P - weight of Q -j- weight of air displaced by 

 Q- 



Log. volume of P = weight in grains of the water dis- 

 placed by P + log. W, - log. (i -P «?,) ; where W, is the 

 ratio of the maximum density of water to its density at t, 

 andt'P/ is the expansion in volume of P at /. (The loga- 

 rithms of these values are given in tables.) 



Log. density of P = log. weight of P in grains — log. 

 volume of P. 



The actual weight of air displaced is to be ascer- 

 tained by the method already stated. 



As the true weight of P in air cannot be ascertained 

 until its volume or density is known, an approximate value 

 of the volume of P may be found by assuming the weight 

 of P to be equal to its apparent weight in air ; and this 

 value of the volume of P may be used in reducing the 

 weight of P, and thus a more accurate value of the volume 

 of P obtained, by means of which a closer approximation 

 to the values of the absolute weight of P, and of its 

 density may be found. This process should be repeated 

 when greater exactness is required. 



H. \V. Chisholm 



( To be continued.) 



