75é 



wall exerts a friction force on the cylindrical surface of the piston, 

 and that in consequence of this the force which drives the piston 

 out must really be greater than the amount which can be calculated 

 from the section of the piston and the pressure. Or in other words 

 the effective area of the piston must be greater than the real section. 

 By means of hydro-dynamic considerations Wagner now comes to 

 the conclusion that the difference will depend on the width of the 

 cylindre in which the piston moves. Half the difference between 

 piston and cylindre section will namely have to be added to the 

 piston section to determine the true effective area. Hence Wagner 

 did not only very accurately determine the piston section, as Amagat 

 did, but also the cylindre diameters (at least for the two small steel 

 pistons which he used). The difference between the two diameters 

 amounted to about 0,01 mm. ; it is therefore by no means insigni- 

 ficant for a total amount of about 5 mm. 



Wagner has, however, also determined the effective area by a 

 direct experimental way, by namely ascertaining with what weights 

 the pistons must be loaded to balance a pressure which is directly 

 measured by means of a mercury column. And he then arrives at 

 a very remarkable result. For whereas the measurement yielded 

 5,128 resp. 4,076 mm. for the piston diameters, 5,138 resp. 4,088 

 for the cylindre diameters, which according to the above would give 

 5,133 resp. 4,082 for the effective area, the direct experimental 

 equation yielded 5,127 resp. 4,076, i.e. exactly the sections of the 

 pistons without any correction. Evidently Wagner has not pointed 

 this out, because in his first investigation the direct experimental 

 determination of the effective area of the large piston of the Amagat- 

 manometer yielded 40,189, whereas the section of the piston itself 

 amounted only to 40.176.'). Tn a later investigation, however, which 

 was undertaken in collaboration with P. P. Koch'), Wagner repeated 

 these determinations. He now finds in measurements which he con- 

 siders more accurate than the earlier ones again 5,128 for the 

 effective area of the small piston, but 40.164 for that of the large 

 one, i. e. even a little less than the real section. Accordingly these 

 determinations cannot give support to the theory of the increase of 

 the effective area in consequence of the friction on the cylindrical 

 surface derived hydrodynamically. '; 



1) I.e. p. 919. 



2) Ann. d. Phys. (4) 31, p. 48. 



^) Some particulars in Bridgman's interesting experiments (Proc. Amer. Acad. 

 XLIV p. 201) seem to point in the same direction, but whether this supposition is 

 true cannot be inferred from the communication with certainty. We shall, therefore, 

 not enter any further into this. 



