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The employment of this rule to find the volume of displacement and the other elements usually tabulated on the displace ment sheet is shown on the attached Tables. The number or stations used is ten, as in the case of Simpson's rule, but for clearness the after body five are indicated by Roman numerals, and the fore body ones in Arabic. The displacement length is 600 feet, therefore by taking the fractions given in the preceding table for ten ordinates and multiplying them by 300, we shall obtain the distance of the displacement sections apart. These distances from the half-length and the sections are here given as used for the Table, but it will be observed that the water lines are spaced to suit Simpson's first rule for the vertical sections as no advantage would be gained' by the use of Tchibyscheff in this direction, owing to the fewer number of water lines generally necessary. The various operations in the Table will be clearly understood from the headlines of the respective columns.

As already pointed out, the great value of this rule is in the calculations to obtain cross curves of stability, specimen tables of which are also given. The fewness of the sections necessary, and the fact that the integrator saves the calculator the tedium of adding up, tells greatly in favor of the adoption of this rule for these calculations both as a time saver and an eliminator of the chances of error.

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A = Distance of Ordinates. : number of stations. t 3=i Simpsons* multiplier.

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