OF THE CKITICAL VELOCITY OF WATER WITH TEMPERATURE. 
47 
a uniform temperature in the pipe increase in a much greater ratio than the increase 
of temiDerature beyond, say, 50° C., and there are other difficulties, due to convection 
and evaporation, which made it desirable to limit the investigation, at any rate for 
the time, to a range of 45° to 50° C. With these limits it was found that the 
decrease or increase of tem23erature along the pipe, when thickly lagged, was 
inconsiderable, and the correction to be apjolied was therefore small and not likely to 
cause an appreciable error. In order to carry on experiments at a higher temijerature, 
it would apj^arently be necessary to surround the experimental tube with a Avater- 
jacket maintained at the same temperature as the Avater in the tank, otherAvise dro2) 
of temperature along the pipe AAmuld be so considerable as to seriously Increase the 
chances of error. 
Method o f Experiment. 
The 251’biciple of the method is the same as originally devised by Osborne 
Reynolds, but the manner of carrying out the Avork differed someAAdiat in detail. 
The method of colour bands is unsuitable for Avater at a high teni23erature, as it is 
impossible to eliminate the effect of conduction and convection, and the AAmter 
consec 2 uently never comes to rest; moreover, ex23eriments by this method lead to a 
different form of the criterion, viz., the maximum limit at Avhich stream-line motion 
is 230ssible, Avhile ex23eriments on the Amriation in the resistance of pipes lead to tlie 
minimum criteiioii, viz., that at Avhich eddies change to steady motion. This latter 
method is also more likely to be accurate, for the maximum velocity of stream-line 
motion depends iqion external causes, Avhich influence it to a remarkable extent. 
Ex23eriments Avere made Avith the tank in the laboratory to discover hoAv far stream¬ 
line motion could be carried under faAmurable conditions; the tank rests directly 
upon the ground, and after Avater at the tem2)erature of the room had l)een alloAA^ed 
to stand therein for tAAm or three days, stream-line motion in 2 )ipes could be maintained 
at higher velocities than that giA^en by the U2323er limit formula for the critical 
velocity viz. ; 
1 /('^) ^ 
43-79 I) 
the units being metres and degrees centigrade, a result no doubt due to the com2)lete 
absence of vibration in the tank, AAdiich AA^as founded on rock, and also the freedom of 
the AA-ater from sediment. 
Moreover, it is easy to loAver the critical velocity by subjecting the Avater to a 
disturbing cause; thus fine matter in sus23ension in the water aauII loAver the critical 
A^elocity. Ta2)2^iRg the pi23e or inter230sing therein a 23iece of Avire gauze Avill also act 
likeAAuse; in fact, the 2^oint of Ijreak-doAvn can be varied Avithin Avide limits 
according to the circumstances. 
Whatever be the disturljlng causes, hoAvever, if stream-line motion exists, tlie 
* ‘ Phil. Trans.,’ 1884, p. 957. 
