484 



Transactions. 



collection of all known experiments on riveted pipe up to the date of the 

 record — viz., 1898 — to which is added a series of thirty-one observations 

 made by the same authors on a riveted pipe 72 in. in diameter and 

 recorded in vol. 44 of the same society. 



In these experiments the speeds vary from a fraction of a foot per 

 second to 20 ft. per second. 



The observations referred to are plotted in fig. 2, and it will be noticed 

 that despite the number and range of observations the range is extremely 

 limited from a law-determining point of view, and one is entitled to say 

 at once on regarding them that no law of friction could possibly be deduced 

 from them, and that every effort in that direction has been a waste effort. 

 The range of log vd/v in these experiments is from 7 to 8, whilst Stanton's 

 observations, before referred to, ranged from log vd/v = 5-2 to log vd/v — 7-2, 

 the extent of which enabled Professor Lees to deduce a law for smooth 

 pipes with some degree of certainty. Even this range could with advantage 

 be extended. 



Fig. 2. 



In the absence of a similar range for riveted pipe it is necessary to 

 consider what degree of guidance Professor Lees's curve, as set out in fig. 2, 

 curve a, afiords towards deducing a resistance-curve for riveted pipe. 



Regarding the plotted points by themselves, all that can be said 

 regarding them is that they indicate an inclination towards the left, but 

 whether a straight line or a curved line would best represent the law 

 no definite answer can be given. 



Most recent experimenters work on the assumption that the law is of 

 the form given in equation (1), which would give a straight line when the 

 logarithmic values are plotted. It will be seen that if the true law is of the 

 form given in equation (2), this would result in a curved line, and inasmuch 

 as any one series of experiments is, as a rule, of an extremely small range 

 from the point of view under discussion, the points would fall very approxi- 

 mately upon a straight line, though in reality such lines are segments of 

 a curve. It follows that as the inclination is different in different parts of 

 the curve, and the range of each series being small, a different index would 

 result according to the position of the series, and which might vary from 



