1816.] On the Stability of Vessels. 139 
By examining the experiments, the result of those with model 4 
at an angle rather less than 30° agrees with the second theorem. 
The result of those with model 4 show the theorem in excess, or 
the angle of inclination must be more than 30° to agree with it. 
Result of experiments with model 8 nearly agrees with the second 
theorem at an angle of 25°; and result with model 9 agrees at an 
angle rather less than 20°, 
By experiments with model 16, it appears that the third theorem 
is erroneous, because in no instance could the metacentre be 
elevated so high. 
Experiments with models 11 and 12 show the fourth theorem 
will not coincide with experiment, unless the angle be more than 
30°. Experiments with model 13 nearly agree with theorem, but 
the experiments are still minus. Model 14, at an angle of 15°, 
nearly agrees with the theorem; and experiments with model 15, 
at an angle between 10° and 15°, agree with the theorem. 
Theorem Fifth.—To ascertain the law of stability, or how much 
«more sail a vessel will carry by augmenting the breadth, compare 
llelopipedons 1 and 4, 1 and 8, 8 and 9, 7 and 9, also models 
16 and 17, 17 and 18, 16 and 18. Suppose the stability to increase 
or decrease, according to some power of the breadth, B d represent 
the breadth; S s, the momentum of the stability, as B™: 1" :: S:s; 
ve Log, S — Log. s 
the exponent m is = Log. B — Log.b° 
5° | LO°} 15°] 20° | 25°} 30° 
3°470)8'458/$-447|3°437}3°428/3-420} land 4, Mean 3°443 of the various value of m. 
4°035|3°631|3*383|3°280/3°321/3°439| land 8, 3°516 
_8°739|3-596| 3-482) 3°428/3°472/3°610| land 9, 3°554 
3°411)3-551)/3-589/3-590|3°639|3-800) Tand 9, 3°586 
3°595'3°233}2°993|2-901/2°967|3°238/16 and 17, 3°154 
3°189/2-980|2°842/2-789)|2°830/2°976)16 and 13, 2°936 
2°739 2-701) 2-675|2:663 2°67 1/2°698)17 and 18, 2°69) 
Ry the above table it appears that the stability of a parallelopi- 
pedon increases in a greater proportion than the cubes of the 
breadth, and that the stability of models 16 and 17 increased in-a 
greater proportion than the cubes; but the stability of modek 16 
and 18 was less than the cubes; and the stability of models 17 and 
18 was still less than that of models 16 and 18. 
The truth of the sixth theorem is corroborated by referring to 
the experiments made with model 16 at an angle of nearly 20°, the 
centre of gravity being at 3 inches ; and to experiments with model 
20 at an angle of nearly 20°, the centre of gravity being at 6 inches. 
The stability of model 16 is greater than the stability of model 20 
‘from 15° to 5°, but less from 20° to 30°. 
That theorem seventh does not agree with experiments, will be 
‘seen by experiments made with models 1 and 8, I and 9, 8 and 9, 
