396 Dr. Eankine on the Statical Stability of a Ship. [March 14^ 



2. When the respiratory orifices are closed, the variations of blood- 

 pressure in the arteries are synchronical with those of air-pressure in the 

 respiratory cavity, and take place in the same direction. 



.3. The increased action of the heart which results from chemical 

 changes produced in the circulating fluid by exposure to air, is of the 

 same nature as the mechanical effect of inspiration, both being indicated 

 by increased arterial tension and acceleration of the pulse. The former 

 may be distinguished from the latter (a) by the length of time required 

 for the production of the effect, and (b) by its dependence on a previous 

 venous condition of the blood. 



4. Hence the influence of the thoracic movements on those of the heart 

 may be either directly mechanical, as in sufl'ocation, indirectly mechanical, 

 as in ordinary breathing, or chemical. 



March 14, 1867. 



Lieut. -General SABINE, President, in the Chair. 



The following communications were read : — 



I. " Note on Mr. Merrifield's New Method of calculating the Statical 

 Stability of a Ship.'' By W. J. Macquorn Rankine, C.E., 

 LL.D., F.R.S. Received February 23, 1867. 



On the 24th of January, 1867, a paper was read to the Royal Society by 

 Mr. C. W. Merrifield, F.R.S., Principal of the Royal SchooUf Naval" Ar- 

 chitecture, showing how, by determining the radii of curvature of the locus 

 of the centre of buoyancy or *' metacentric involute" of a ship in an up- 

 right position and at one given angle of inclination, a formula may be ob- 

 tained for calculating to a close approximation her moment of stability at 

 any given angle of inclination, on the assumption that the metacentric invo- 

 lute can be sufficiently represented by a conic. 



It has occurred to me that the latter part of the calculation in Mr. Mer- 

 rifield's method might be simplified by assuming for the approximate form 

 of the metacentric involute, not a conic, but the involute of the involute of 

 a circle ; the locus of its centres of curvature, or " metacentric evolute," 

 being assumed to be the involute of a circle. 



The involute of the involute of a circle is distinguished by the following 

 property. Let r be the radius of the circle, that radius of curvature of 

 the involute of the involute which touches the involute at its cusp, and p 

 another radius of curvature of the same curve making the angle Q with the 

 radius ; then 



p=p.+ ^- ' (1) 



Having found, then^ the radii of curvature of the metacentric involute in 



