MODERN STEAM PR ACTICE.

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Obviously, the formula may be written--

c|=MV> (I)

in which it is asserted, the true form of C in the first member isunknown, and the quantities represented by the factors M, and V 2of the second, are, at best, but rudely approximate.

It has been stated by me that a better approximate form for thefactor expressed by M in the Admiralty formula is the quantityLVm, that is to say, the product of the length of the vessel into thesquare root of the immerged midship section; only, to meet acorrection necessitated by the known fact that when uninfluencedby restricted depth of water, small vessels experience greater pro-portional resistance than larger ones, and also corroborated byD’Arcy’s exhaustive experiments on the flow of water, in which itwas shown that the diameter of the pipe entered inversely as anelement of the resistance. It was therefore proposed, as a practicalbut empirical correction, to take the J^th power of this quantityinstead of its full, value, and hence, on this hypothesis, the quantityb comes to be represented by the approximate value—

h JWm)^

c

In which C is a constant involving a number of factors, and corre-sponds to, but is not the same as the C of the Admiralty formula,and thus we finally arrive at the following equation—

y = —g—- log. 1 a V. (3)

The factor log . -1 «V of the second number being the notation bywhich is expressed, the number wJiose common logarithm is the pro-duct of a small quantity, a, into the speed, V knots.

The crucial practical test of the accuracy of the speed factor ofthe second member, is to apply the formula to the progressive speedtrials of actual steam vessels. For, taking the common logarithmsof both members, and with the speeds taken along an axis as

abscissas, if we set up the values of the first number log. y, as ordin-

ates; these values will ränge in a straight line, inclined to the axisat an angle dependent upon the value of a, and having the Ordinate

at the origin equal to the value of the factor log. —or, simply,

log. b; whence, by measurement and calculation, or calculationalone, it is easy to obtain the value of C, which will be found a