TKANSACTIONS OF THE SECTIONS. 247 



It must be clear to any unbiassed mind that a method which is of absolute im- 

 portance in the trials of models, can be of no less need in the concrete trials of 

 ships' engines and propellers made on the mile. Of course, curves of revolutions 

 per minute, ship percentages and constants, according to any formula, can also be 

 set off wth the simple speed and power curve. 



Such curves were shown in the diagrams illustrating this paper, and included, 

 besides specimens of trials conducted by the author's firm, others conducted by 

 Messrs. A. and I. Inglis and the Admiralty. 



The constant cm-ve shown in each case was set off" to tlie numbers of the Ad- 

 miralty midship-section formula, but represented equally well, with suitable scales, 

 the Admiralty displacement and Prof. Rankine's augmented surface constants. 

 Had the theory been true that the power reqmred for propulsion varied as the 

 cube of the speed, these constants would not have been curves but straight lines 

 parallel to the base of the diagram. As they were very marked curves, and, indeed, 

 liir removed from any approach to horizontal straiglit lines, .they indicated an 

 equally great fault in all the three formula). An examination of the cm-ves showed 

 this fault to be the acceptance of the fallacious theory that the power varied as 

 the cube of the speed. 



In none of the diagrams and in no progressive series of trials submitted to the 

 author had this fallacy even the shadow of a sound support ; and had Professor 

 Rankine known the extent and worthlessness of it, he would never have been 

 tempted to prove his theory underlying the augmented surface formula from the 

 ' Warrior's ' highest speed trial, as two other trials exist, taken at the same draughts 

 and within a few days of each other, which contradict it. In one of the speed- 

 curves shown to the Association, the horse-power varied from ratios in the square 

 to ratios nearly in the fifth power of the speed. 



Had Professor Rankiue possessed such sets of trials as the practical world 

 should have supplied him with, his great skill would have doubtless drawn from 

 them some very valuable teachings, instead of the formula of the auo-mented 

 surface, which for every purpose (seeing a comparison of steamers is rendered im- 

 possible by our ignorance of their progressive speeds and powers) is of no more 

 value than the Admiralty formulae it was intended to supersede. Beyond this 

 these curves go to prove that in the expenditure of power in relation to speed, 

 within the limit of the liighest ocean speeds now in use, marked speeds pecidiar 

 to the vessel are seldom likely to be apparent, excepting tliey be foimd by some 

 such empirical formula} as those referred to. These formulte show apparent speeds 

 of maximum efficiency ; but they are only apparent, and depend upon the theoretical 

 power of the speed in which the horse-power is supposed to vaiy. Different speeds 

 of apparent maximum efficiency will appear as the square, the cube, and the fourth 

 and fifth powers of the speed are selected. 



Indeed if we are ever to get a tolerably good formula, for finding speeds and 

 power, which is doubtful, it will not be found without progressive trials combined 

 with and checked by such experiments as Mr. Fronde is now making on models. 



Regarding the conduct of progressive trials, it is of primary importance that 

 their accuracy in all parts should not fall below the Admiralty standard, and that 

 a calm day shoidd be chosen for their performance. The wind has a most disturb- 

 ing influence on the slow speeds. In the engine-room, the head of it must not 

 only control his obser^dng staff, but must carefully regulate the development of 

 power on each pair of runs. Any great inequality will vitiate the results of the 

 trials. In fact progi-essive trials without honesty and accuracy will be failures. 



A small copy of the speed-power, revolution, Admiralty midship and section 

 constants, and ship percentage curves of the screw steam-ship ' Taupo,' built and 

 tried by the author's firm, is appended (see fig. 5, Plate XIII.). After the remarks 

 already made, this diagram will be clear. Small circles mark the points of mean 

 speeds observed on trial. 



JVote.—Mr. Denny's paper is printed in full, with the original diagrams, in 

 ' Engineering,' for October 15th, 1875, vol. xx. p. 311. 



