1824.] Stability of Floating Bodies. 83 



the vessel, were calculated in ounces, drachms, and scruples, 

 and afterwards reduced to the decimal parts of an ounce, three 

 scruples in this case being equal to one drachm. 



Example 1. — Model 1. — Experiment 1. — The total depth of 

 the model being 7*1 inches, the height of the centre of gravity- 

 is subtracted in each experiment, and the length of the mast 

 (measuring from the centre of gravity of the model to the apex), 

 20*96 inches being afterwards added, gives the length of lever 

 at which the weights are applied to produce the various inclina- 

 tions of 5° 10°, 15°, 20°, 25°, and 30°, Ther. The centre of 

 gravity in Exper. 1 being situated two inches above the bottom 

 of the model, and coinciding with the centre of gravity of the 

 displaced fluid, the weight 2*2239 oz. being applied to the mast 

 will incline it 5°. It is obvious that to restore the vessel to its 

 original vertical position, the momentum of the water must be 

 equal to that of the inclining power. If, therefore, the momen- 

 tum of the effort to incline the vessel (that is to say, the weight 

 applied, multiplied by the length of the mast) be divided by the 

 weight of the displaced water, the quotient will be the length of 

 lever E R on which the water acts. 



Experiment 1. — Model 1, inclined 5°. — The inclining weight 

 is 2*2239 ounces, the length of lever 26-06 inches, and weight 



of the displaced water 324*52 ounces, then = *18 



or E R. By proceeding in a similar manner, the length of lever 

 is obtained for 10°, 15°, 20°, 25°, and 30°. It should be men- 

 tioned, that after the vessel had been inclined on one side, it 

 was turned and inclined on the other, by which means if the 

 mast was not perpendicular, or there was any inaccuracy in the 

 form of the model or manner of placing the ballast, it was imme- 

 diately perceived, and the error corrected in taking the mean of 

 the two experiments. The difference, however, seldom amounted 

 to two drachms, and in general was much less. 



The result of the second set of experiments proved the accu- 

 racy of the first, the altitude of the point M being nearly the 

 same in both cases, as may be seen on reference to the annexed 

 tables. 



Column 1 shows the angles of inclination. Columns 2 and 6, 

 the weights that produced that inclination. Columns 3 and 7, 

 the length of lever E R and G r. Columns 4 and 8, the lever 

 E R and G r, calculated by Mr. Atwood's theorem. Columns 

 5 and 9, the height of the point, M above the point E, and 

 found in the following manner : — As the sine of the inclination 

 : E R or G r : : radius : EM or G M. When the centres of 

 gravity of figs. I and 7 coincide with the centres of gravity of 

 the displaced fluid, their stability, allowing for the attendant 

 inaccuracy of experiments, will be the same as shown by the 

 subjoined calculations. 



g2 



