58 MM. A. Kuudt and E. Warburg on Friction 



correctness of the theory, cannot be strictly demonstrated from 



the experiments, since - is everywhere too small in proportion 



to 1 ; but if the theory be assumed, the constancy of the friction- 

 index fju down to 1*5 millim. pressure is proved by these experi- 

 ments. 



On proceeding, further, to investigate the laws of gas-friction 



below the before-mentioned limit of rarefaction (- 7 >^-r), we 



could not succeed, even with the most careful drying, in remo- 

 ving with sufficient completeness the last traces of aqueous 

 vapour, which, insensible in the above experiments, with the low 

 pressures here employed distorted the results. The presence of 

 aqueous vapour was shown inter alia by this — that the damping- 

 moment for a vacuum (so we name a space filled with a gas of 

 T i ¥ of a millim. pressure mixed with vapour) rose considerably 

 when the apparatus was left to itself. This arose from water 

 separating from the solid parts and evaporating into the vacuum. 

 In consequence of this, the theory cannot be quantitatively tested 

 on the results obtained. Nevertheless the following series of 

 experiments shows how far we were able to reduce the loga- 

 rithmic decrement \ by rarefying the gas. The thickness of the 

 friction-stratum amounted to 1 millim. 



Hydrogen. 



June 30. 760 millim*. 0-0387 



Vac. I. 0-0180 



Vac. II. 0*0140 



Vac. III. 00119 



July 1. „ 0-0220 



Vacua II. and III. were obtained by causing the little gas- 

 bubble to pass out of the receiver of the mercury air-pump into 

 a vacuum, until at last, with vacuum III., nothing more passed 

 out, even into that. Hence vacuum III. is probably to be re- 

 garded as an aqueous-vapour vacuum, in which the mean length 

 of path is much greater than T \ d. Through the taking away 

 of very slight traces of hydrogen (vac. I. -vac. III.) the logarith- 

 mic decrement sinks to § of its value. From this we see how, 

 in accordance with the gas-theory, proportionally large quanti- 

 ties of magnitude of motion can be conveyed in the unit of time 

 by traces of gaseous matter. 



Heat-conduction. 

 If we contemplate the simplest case of heat- conduction, in 

 which a layer of gas without weight is included between two 



