116 PKOCEEDINGS OF THE AMERICAN ACADEMY. 



The progress made in the solution of these problems up to the 

 present may be summed up as follows : 



(1) The great difficulty in devising and carrying out methods of con- 

 structing the pieces of apparatus required has been overcome. This, 

 which was by no means the least difficulty encountered, can be appre- 

 ciated only when one knows the form of the apparatus required, and 

 the treatment which the apparatus must receive in order that all traces 

 of moisture may be removed from all the solid surfaces exposed to the 

 interior of the containing vessel. 



(2) The friction has been measured at pressures ranging from that 

 of an atmosphere to 0.00024 mm. of mercury, the small pressures being 

 measured by the McLeod gauge. Figure 6, in which ordinates are 

 proportional to friction and abscissas proportional to pressure, shows 

 how the friction diminishes as the pressure diminishes. The curve, 

 whose error is certainly less than one per cent (if the McLeod gauge 

 can be considered trustworthy over the range of pressures indicated), 

 is very regular; and a discussion of the numerical results in that 

 part of the curve which corresponds to pressures above 0.1 mm. of 

 mercury shows that the law 



[tz:T-']^' = '' 



first deduced by Kundt and Warburg for pressures down to 0.6 mm., 

 holds very well down to about 0.1 mm. Beyond this point, however, 

 the theoretical curve, i. e., the curve obtained by calculating p from the 

 above relation after the constants have been determined from obser- 

 vations at comparatively large pressures, does not coincide with the 

 actual curve. 



(o) The force due to transpiration has been measured over a range 

 of pressure varying from 1.42 mm. to 0.0093 mm. 



(4) Figure 7 (the error in the curve may very well be five per cent), 

 in which the ordinates are proportional to the transpiration force and 

 abscissas to pressure, shows that, for pressures below that for which 

 the force is a maximum, the relation between the force and the 

 pressure rapidly approaches a relation of mere proportionality, or 

 at worst a proportionality disturbed by a constant term. In other 

 words, the curve becomes a straight line passing very nearly through 

 the origin. 



