414 Mr, Herapath on the Causes, Laws, and principal [June^ 



tiifiin;^ difference in the ratio of the temperatures, which a con- 

 siderable thermometric difference in the two hemispheres would 

 produce, conspire to show that the coefficient of such an equation 

 must be exceedingly small, if not wholly insensible. 1 have, 

 therefore, merely alluded to the subject, that philosophers might 

 take an opportunity of considering it further, and of examining 

 whether in the future improvement of the lunar tables, the une- 

 qual temperature of the different hemispheres, and the alternate 

 increase and decrease of temperature in the same place, arising 

 from the motion of the sun, are deserving of attention. 



Returning to our law of gravitation, it is found that when the 

 diameter of the attracted particle bears any sensible proportion 

 to the central distance of the two particles, its gravitation, except 

 in the case of its being a sphere,*" no longer follows the law of 

 the inverse squares of the distances, but a law, which increases 

 the force of attraction much more rapidly as the particles 

 approach. It is, therefore, evident that our theory of attraction 

 is not only capable of expounding the gravitation of bodies at a 

 great distance from one another, but also all that variety and 

 increase of force which are observed in the particles of bodies 

 when brought nearly into contact. For instance, if two particles 

 approach each other with flattened surfaces, the intensity of 

 their attraction when these surfaces are very near to each other, 

 and the force of their cohesion when the particles are in contact, 

 will be much greater than if the same particles could have pre- 

 sented spherical or more pointed surfaces, so as to touch but in 

 one or two points. For the same agitations of the same particle 

 will rarify the ethereal medium considerably more on the flat- 

 tened side of the particle than on the pointed side (generally 

 indeed more than in proportion to the greatest transverse sec- 

 tions of the particles); and, therefore, when the particles 

 approach with their flattened sides, the medium between them is 

 much more rarified, and its elasticity, therefore, much more 

 diminished than they would be under similar circumstances of 

 agitation between less superficial areas ; and consequently the 

 attraction of the particles, which consists in the excess of elasti- 

 city on the exterior and interior surfaces, is considerably 

 augmented. And when the particles come into absolute con- 

 tact, the flat sides, by displacing a greater portion of the medium 

 from between them, will occasion the particles to be pressed 

 together by a force, which, instead of being equal to about the 



♦ Were the particles of fluid bodies nearly spherical, and were it by forces recipro- 

 cally proportional to the squares of their central distances that they are kept together, 



we should have (S,^ — S*) Q = <, S,^ — / S^ ; in which f„ <, are any two tempera* 

 tures, /, being the higher, lS„ S, the corresponding volumes of the fluid body, and Q an 

 arbitrary quantity to be determined from the nature of the fluid. But the expansions 

 determined from this formula are manifestly too little; since, if the particles attract one 

 another with such forces, the fluid can never become gaseous. The true law of expan- 

 sion in fluid and solid bodies, I can easily perceive, is connected with a gaseous problem 

 which I have not yet resolved. 



