1816.) On the Stability of Vessels. 187 
lever on: which»the fluid;acts, which; for the sake of distinction, call 
x. Then,} to find the greatest height, the centre’ of gravity of the 
model cam be raised above the. bottom without oversetting (called 
by the French writers on aval architecture the metacentre), \ as 
30°: x or 907582: radius:+-1°8152, or the height of, the meta- 
centre above the centre of gravity, which call y Then 2 inches, 
the height.of the model’s centre of gravity, added to 1°38152, the 
sum, 378152 is the altitude -of the metacentre, according; to this 
experiment, above the bottom of the model. By, the same process 
the height of the metacentre was obtained, when the experiment 
was madeat 10°, 15°, 20°, 25°. To ascertain more exactly the’ 
height of the metacentre, the centre of gravity .of the figure was 
raised. In Exper. 2, the height of the centre of gravity was raised 
to 2°25 inches above the under side of the figure ; and in Exper. 3, 
to 3 inches. By these two, the accuracy of the first experiment. 
was corroborated. Three heights are thus obtained. But from the 
unavoidable . inaccuracies to which experiments are liable, these 
numbers differ; therefore take the mean of the heights of the 
metacentre thus determined, | But as these means, when compared, 
are found neither to increase nor decrease in a regular manner, take 
the differences between each set of experiments; and then take the 
mean of all the differences, and examine which of the differences 
most nearly coincides with the mean difference. The two experi- 
ments whose difference is the nearest to the mean difference are to 
be considered as the best experiments. Then, by adding and sub- 
tracting the-mean common difference, the whole will be brought 
into a regular series, and the irregularities corrected. The following 
example will more clearly explain the process. In Table 3, are set 
down the various heights of the metacentre at every angle of incli- 
nation, as determined by Exper. 1, 2, and 3; and the fourth hori- 
zontal line contains the mean results. In the eighth right hand 
vertical column are placed the differences of the mean heights. 
The mean of ‘the five differences is °0538. The nearest difference 
to this number is ‘0584, which is the difference between the mean 
height of the metacentre at 15° and 20°. . By taking the mean of 
the experiments at 15° and 20°, 35995 — 3°6579 = 3°6287 ; and 
adding and subtracting half of -0538 (which is -0269) to 3-6287, 
the numbers 3°6556 and 3°6018 are obtained, which are the cor- 
rected heights of the metacentre. Then by adding +0538 to 3°6556, 
and subtracting the same from 36018, the corrected altitudes of the 
metacentre are obtained, which are set down in the last column on 
the right. By subtracting the altitude of the model’s centre of 
gravity from these numbers, a more accurate value of 7 is obtained. 
(See Table 4.) Then with the value of y, and the angle of inclina- 
tion of the model, the length of x is obtained. This number mul- 
tiplied by 559°06, the weight of the displaced water, gives the 
momentum of the stability. This number divided by the length of 
lever which inclined the model, gives those numbers called the 
regular series ; and according to the agreement or non-agreement 
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