394 Scientific Proceedings^ Rojial Dublin Societij. 



On no occasion was it found possible to locate the discontinuity for the 

 copper tube (l"9 em. bore). This seems the most peculiar fact connected 

 with it. As for the wide (7'4 cm.) tube, also of copper, it was not possible 

 with the fan at our disposal to reacli the speed of over 203 cms. per second 

 mean velocity where this tube miglit liave been expected to give it. 



A tliird possible explanation may be found in something of the nature of 

 "slip." It could very well be imagined to result in tlie same law, equally 

 well during stream-line and turbulent motion. Measuring as we do the 

 mean velocity of the blast, the velocity so measured, where slipping would 

 take place, would not necessarily depend on wlietlier the greater mass of 

 the gas was moving according to stream-lines or not. What we should 

 take into account would be tlie viscoxis drag ou tlie walls, or on tlie layer 

 of gas condensed on the walls. The question arises, of course, what is 

 meant by " slip," in such a case. The most probable phenomenon to expect 

 is something of the nature of ordinary turbulence, but in the layers 

 nearest the walls of the tube. A sort of rolling motion of the gas-layers - 

 may set in here instead of a sliding. For the same volume delivered, if no 

 " slipping " took place near the walls, the maximum velocity in the gas must 

 be greater than with slipping. Thus, since the ionisation measured at B 

 depends on the time required to come from ^ to i? as well as on the volume 

 of air coming down the tube, if the volumes increase only slightly while the 

 average time is not decreased sufficiently (which would occur if slipping had 

 meanwhile begun), then the velocity-ionisation curve would commence to 

 slope upwards less rapidly at the critical point in question. 



Let us for a moment consider the flow in a narrow tube. For, although 

 our tubes are by no means narrow, yet some idea of the conditions existing 

 before turbulence sets in may be gained from the case of narrow tubes. 



It is easy to show that if v,,, is the mean velocity of tiie whole gas at any 



cross-section of the tube, since 



V 



i\n = — ;. 



TTCr 



we have 



fdv\ 



drjr -- n ^ _ 4 (tjj 



but we have seen (formula 8) tliat when the second " discontiuuitj' " occurs 



dv 

 for air (r„, - 16) is approximately proportional to the radius a. Hence — 



at the surface would be a constant in any tube for a velocity 16 units less than 

 the " critical " velocitj'. Of course it is obvious that this argument assumes 



