146 DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



86. Remark on Unit-Tubes. In sections 72 and 73 we have developed some 

 properties of the isobaric-isosteric unit-tubes, formed by the intersection of the iso- 

 baric and the isosteric surfaces. It is important to remark that these properties are 

 retained by the tubes whose cross-section is seen in figs. 30 and 31, nothing being 

 changed by the fact that surfaces of equal-volume anomaly have been used instead 

 of the true isosteric surfaces to define the tubes. To show this we remark that the 

 " normal " specific volume is constant all along an isobaric sheet, the anomaly only 

 varying. Consequently we get unit-change of specific volume and unit-change of 

 thickness of the sheet for every volume anomaly met with, these surfaces being 

 drawn for unit-differences of the specific volume. Instead of counting the surfaces 

 we can count the tubes. Further, the variation of the total specific volume and the 

 anomaly going always in the same direction, we can use the same rule for the signs 

 of the tubes, based upon the direction of the projection on the isobaric surfaces of 

 the ascendant of the true specific volume or of its anomaly. 



We can therefore use the expression isobaric-isosteric unit-tubes irrespectively 

 of their being defined by true isosteric surfaces or surfaces of equal-volume anomaly. 

 In both cases the algebraic counting of the tubes will give the change of thickness 

 from place to place in an isobaric sheet and the horizontal course of the tubes 

 within the sheets will be given by charts like those of fig. 28, giving the topography 

 of the surfaces limiting the sheet relatively to each other. 



The isobaric curves in figs. 30 and 31 being drawn for the interval of 1 centibar, 

 and the curves of equal-volume anomaly for intervals of 0.000 1 m 3 /ton, each paral- 

 lelogram in the figure will represent 0.0001 unit-tube. The curves on the charts 

 of fig. 28 being drawn for intervals of 1 dynamic millimeter, the interval between 

 the successive curves will represent 0.01 unit-tube. 



What we have thus said of the isobaric-isosteric unit-tubes may, the terms being 

 properly changed, be applied to the equipotential-isopycnic tubes, whether they be 

 defined by the true isopycnic surfaces or by surfaces of equal anomaly of density. 



