26 



MR J. Y. BUCHANAN ON THE 



also most carefully determined once for all, so that at any moment the total weight of 

 the displacing instrument is accurately known." * 



A- 



-D 



Section II, — The Principle and Construction op the Closed Hydrometer. 



§ 9. It will be convenient to follow in detail the preparation of the hydrometer 

 for use. 



The instrument being closed, its true weight is constant. 



Let it be assumed that our experiments are actually made in vacuo, 

 at the sea-level in lat. 45°. In these conditions the standard gram exerts 

 a vertical pressure of 1 gram (true). 



We weigh the hydrometer and find its weight to be W grams. We 

 now float it in distilled water contained in a suitable cylinder. In the 

 construction of the hydrometer the internal load has been so adjusted 

 that, when immersed in distilled water of the standard temperature T, 

 which is to remain unaltered during the whole of the experiments, the 

 surface of the water shall cut the stem in some line C, near its junction 

 with the body of the instrument. Then the weight of the water displaced 

 by the hydrometer is exactly W grams. 



Let pressure be now applied to the top of the stem, A, until it is 

 completely immersed. Let the measure of this pressure be w grams. 

 Then the weight of water displaced by the instrument when totally 

 immersed at temperature T is (W + w) grams. 

 \ / We assume that the stem is a uniform cylinder of circular section and 



X^ ^ terminated by a plane surface. If we apply pressure so as to immerse 

 y^ ^v. the stem to the line D, which is midway between A and C, the pressure 



i^HI^BI required will be — grams ; and, if the portion of stem so immersed, CD, 



stands in any other ratio to the total length CA, the pressure required to 



produce the immersion will stand in the same ratio to w. 



Let the experiments be made in air of temperature T, and of pressure and humidity 



such that 1 cubic centimetre of it weighs 1 '2 milligram. When the experiment was 



made in the vacuum and the surface of the water cut the stem in C, the weight of the 



water so displaced was exactly equal to that of the hydrometer, namely, W grams. 



After air has been admitted, the surface of the water no longer cuts the stem 

 exactly in C, but at a point a little lower. This difference between the lines of flotation 

 is due to the fact that, while experimenting in vacuo, the portion of the stem which is 

 not immersed in the water is immersed in a medium the density of which is insensible, 

 whereas, after the air has been admitted, it is immersed in a medium of which 1 cubic 

 centimetre weighs 1"2 milligram, and this exerts an upward pressure, in opposition to 



Report of the Sixth International Geographical Congress, held in London, 1895, p. 412. 



