EXPERIMENTS ON THE FROUDE. 103 
rate, especially when a boat is driven at high speed. The estimate of the 
effect of the discrepancy in question is difficult and uncertain and as 1 or 2 
per cent. is not very important for our present purpose, I have preferred to 
‘let it go with other discrepancies. 
To enumerate the several elements that may enter into an analysis of 
the discrepancy we have: 
1. The computation of surface-friction resistance. No data has been 
published since that by William Froude in 1888; though not published it 
is well-known that modern experiments on paraffine and varnish for models, 
give close concordance with his values. But all quantities offered for com- 
putations for ships are extrapolated from Froude’s results that were on 
surfaces not over 50 feet long. Tideman’s quantities used in the analysis 
of the Manning were deduced by him from Froude’s paper and in my opinion 
are unquestionably too high. Plausible values could be assigned that would 
close the gap of our discrepancy. 
2. The steam-engine indicator is notoriously unreliable, 2 or 3 per cent. 
being a conservative estimate of probable error. The tendency with piping 
to a three-way cock is usually toward underestimating power. 
3. The estimate of hull-efficiency from wake and thrust-deduction is 
open to doubt, and I must admit that my estimate is as favorable as cir- 
cumstances indicate. 
4. Though the theory of mechanical similitude indicates that resistance 
is proportional to the density of the medium and therefore it is customary 
to allow an increase in the ratio of 
35 336 
for ships in sea-water we have no experimental information on this point. 
5. There is reason for questioning the accuracy of the mechanical theory 
of similitude as applied (a) to the computation of residual resistance and 
(b) to the properties of propellers, more especially as the pressure of the 
atmosphere is nearly constant and does not vary as the theory would indicate. 
In conclusion it may be said that an estimate could be made of the 
influence of each element, which would be plausible if not probable, in such 
a way that the entire discrepancy could be explained away, but the operation 
would be more ingenious than ingenuous. 
TESTS OF IQII. 
Since the investigation of 1910 showed such an unexpectedly large 
influence from the broad stern-post it was decided to fit a fair-water to give 
