308 Mr MOSELEY, ON THE 



Two masses, therefore, thus placed together would remain in equi- 

 librium, without the aid of any external force, and by reason only of 

 their mutual pressures and the resistance of their abutments. 



It is also evident that since the line of pressure is similarly situated 

 in both, they cannot be thus placed together so that their lines of 

 pressure may meet and have a common tangent at the point where 

 they meet, unless both lines of pressure be perpendicular to the com- 

 mon surface at that point. 



This condition throws two new equations into the system, and de- 

 termines the value of P' in terms of a single variable. 



The value of P' is not in this case that which we have called 

 the absolute minimum or minimum minimorum, but simply the greatest 

 or least force, which applied at a given point, in a given direction will 

 support the system. 



If however instead of a single point of contact we suppose the 

 masses to be in contact throughout the whole surfaces of two planes, 

 it is evident that the point P' * will take up for itself that position, 

 which we have supposed to correspond with the absolute minimum ; 

 a condition to which the form of the line of pressure, and the 

 position of its point of contact with the surface of the mass, will also 

 be subjected. 



Hence it appears that two masses, thus in contact throughout the 

 surfaces of two planes, sustain a less aggregate of pressure, on their 

 common surface of contact, than two similar masses in contact only 

 by a single point, unless that point, and the position of the masses, 

 be such as to correspond to the minimum minimorum. 



In the preceding pages we have supposed the form of the solid 

 to be given, together with the positions of the different sections 

 made through it, and we have thence deduced the form of its line 

 of pressure and the direction of that line through its mass. 



. ?;* The point P is here the point of application of the resultant of the resistances on 

 the different points of either plane. .:iorte«pi sJi -^..rnaHb 



..H .Ui T ■ 



