VOL. LXXXVl.] PHILOSOPHICAL TRANSACTIONS. 698 



pass through a position of equilibrium ; yet there seems reason to suppose that 

 in some vessels the stability increases to a maximum, and afterwards decreases 

 when the angle of inclination is farther augmented : whenever a vessel of this 

 description shall be inclined beyond the angle where the stability is greatest, the 

 following consequence must necessarily ensue ; if the angular velocity should 

 be considerable, the rolling of the ship will be extended to large angles of in- 

 clination, because when the stability is more and more diminished as the angle 

 of inclination is augmented, more time will be required for the diminished. force 

 to re-act against the ponderous mass of the vessel, in order to restore it to the 

 upright. It is certain that the angle, as well as the celerity or slowness of roll- 

 ing, depend on other elements, as well as on the stability, particularly on the 

 weight and extent of the masts and sails, and the position of the ballast and 

 lading : but in comparing the vibrations of the same vessel through different 

 arcs, those elements are the same, while the force of stability alters continually 

 as the angles of inclination are increased or diminished. 



These alternate vibrations of a ship in rolling have been deemed analogous to 

 the oscillations of a pendulum ; and in order to reduce to some kind of measure so 

 essential a quality of vessels, Bouguer and other writers propose to find a pen- 

 dulum isochronal to the oscillations of a ship. This problem seems to impiv 

 both that the pendulum sought, and the vessel itself, shall vibrate in arcs that 

 are extremely small ; for otherwise the analogy altogether fails: no oscillating 

 body can describe arcs of unequal lengths in equal times, unless it is impelled 

 by forces which are in the direct ratio of the distances from the quiescent point ; 

 and therefore the oscillations of a vessel vibrating in different finite angles are 

 evidently not isochronal with each other, since the force of stability varies in a 

 proportion so different from that of the distances from quiescence ; nor can they 

 be isochronal with any pendulum, unless the arcs of vibration are of evanescent 

 magnitude ; in which case the force of stability being in the direct proportion of 

 the angles of inclination from the upright, has the effect of producing an 

 equality in the times of oscillation : to ascertain a pendulum vibrating in small 

 arcs which is isochronal to the oscillations of a vessel, under these restrictions, 

 is a problem which may be solved with sufficient exactness ; but unless the 

 limitation above-mentioned should be specified, it is a question without the ne- 

 cessary conditions. Buuguer in his chapter entitled, que les Oscillations sont 

 Isochrones, does not expressly n)ention this limitation, but we must allow it 

 probable that he conceived it to be implied. 



From the reasons that have been stated it seems to follow, that in order to 

 form a satisfactory opinion of the qualities and performance of a vessel at sea as 

 depending on the plan of its construction, the farces of stability at the several 

 angles of inclination from to the greatest limit ought to be ascertained, parti- 



