210 
MESSRS. T. E. STANTON AND J. R. PANNELL ON SIMILARITY OF 
not large, viz., from 48'0 (the critical velocity) to 469 cm. per second in the 0'62 cm. pipe, 
and from 23 (the critical velocity) to 705 cm. per second in the 1*27 cm. pipe, and 
further, that the difficulties in maintaining a uniform speed in these experiments, 
owing to the fact that the water was drawn direct from the Manchester mains, were 
such as to render any small variation from the index law, such as would exist over 
such ranges of speeds, almost impossible to detect. In Froude’s experiments* on 
towing Hat hoards the range in speed was not greater than from 50 to 500 cm. per 
second, so that no deviation would be apparent. 
In the case of the present experiments the results for the 1 '255 cm. pipe were taken and 
according to Reynolds’s method, the logarithms of the friction and velocity from v = 40 
tov = 100 cm. per second were carefully plotted. The points so obtained were found 
to lie on a straight line whose slope was 1*72 to 1. Assuming a law of resistance 
R = kv n , where n had this value, h was determined from the low speed observations 
used for the determination of n and a series of values of R were calculated up to a 
speed of 3200 cm. per second. Plotting these values and those actually obtained in 
the experiments the two curves in fig. 4 were obtained, from which it will be seen 
that by the use of the index law the resistance is underestimated by 5 per cent, at 
* ‘B.A. Report,’ 1872, p. 118. 
