caused by atmospherical Refraction. 241 



equal, the deviations will be as the refracting forces, i. e. as the 

 increments of density. 



Prop. ir. When two fluids of unequal density are brought 

 into contact, and unite by mutual penetration ; if the densities 

 at different heights be expressed by ordinates, the curve which 

 terminates these ordinates will have a point of contrary flexure. 



For the straight lines da, rn, (Plate IX.) Fig. 1. which ter- 

 minate the ordinates rx, dy, of uniform density, will be parallel, 

 and, if not united by contrary curvature, some straight line of 

 union, as ao, must be supposed. But, from whatever cause the 

 first line a is inferred, by the same cause other intermediate 

 lines mp, tq, &c. will be produced, and curves defm, mtsr, 

 will be ultimately formed, having a point of contrary flexure 

 at m. 



The form of the curve does not appear to admit of accurate 

 investigation, nor is it of importance to the subsequent reason- 

 ing, if wholly unknown. We may, however, form some judg- 

 ment of its nature; for, whether the densities depend on 

 different specific gravities of different fluids, or on unequal 

 temperatures of different portions of the same fluid, the curves 

 will be nearly alike. 



In each of these cases, to whatever small distance pc, Fig. 2, 

 the mutual attraction is sufficient to occasion intimate union of 

 the fluids, the density mn of the mixture will be an arithmetic 

 mean ; and, for the same reason, at any intermediate smaller 

 distances, there will be a series of arithmetic means ef, gh, &c. 

 interposed, and the line a 0, uniting the ordinates, will be straight. 



By progressive effect of this attraction, and successive inter- 

 polations, in Fig. 1, curves defm, rstm, will be formed, of which 

 the straight lines mp, tq, &c. are tangents. 



lis 



