248 Researches in the Theory and Calculus of Operations. 



impulsion, each impulse would add its effect to the sum 

 of those already existing, and there results a uniformly ac- 

 celerated motion, such as is produced by gravity. 



!N~.B. Throughout all these inquiries, it is understood that 

 the whole sphere is in action, the result of which is as if the 

 entire force were concentrated at the centre (Laplace). 



6. From the molecular to the planetary spheres in mag- 

 nitude, each sphere is amass of concentric ensphered shells 

 of emanating force, each atom of the shells pressing in the 

 direction both of the normal and of the circumference. In 

 equilibrium (fig. 5), the diametral and circumferential pres- 

 sures of every pair of complementary hemispheres ABA' 

 and A'B'A, BA'B' and B'AB, etc. are equal and opposite. 

 The entire sphere, of which ABA'B' is a diametral plane » 

 section, is built up in like manner as each of its atoms; and 

 all is in equilibrium, not only within the sphere itself, but 

 with the medium by which it is surrounded, the atoms of 

 which are represented by dotted circles in contrast to the 

 darker lining of the sphere. 



In a mathematical inquiry into the effects of the mole- 

 cular forces, it has been shown by a celebrated analist that 

 the equation that convenes to the successive spherical shells 

 from the centre to the circumference, has to be modified at 

 the surface to meet the different effect of the force of the 

 medium surrounding the sphere, in order that equilibrium 

 may subsist between the sphere and that medium (Poisson). 

 Each atom on any shell must be in equilibrium not only 

 with iis tmmediate right- and lefthand neighbors situate 

 both on the diameter and on the circumference, but also 

 through communication with its opposite atom equidistant 

 from the centre. The circumferential atoms of the surface 

 of the sphere should also be in equilibrium with the im- 

 mediately surrounding atoms of the medium ; but as the 

 medium has less density than the solid sphere, such equili- 

 brium cannot directly subsist. The difference of tension is 

 propagated across the diameter (from A to A'), and is there 



