26 REPORT — 1839. 



By combining these equations with those which assign the law of 

 motion, it is always possible to eliminate all the differentials if the 

 number of points (n) be taken great enough ; and when we assume 

 (as in all physical applications to general laws of force we must,) that 

 the distance between every two points is the same function of the 

 masses, positions and motions of the rest, it may be effected in a simple 

 manner. 



On certain Results, regarding the minimum thickness of the Crust of the 

 Globe, which might be consistent with the observed phcenomena of 

 Precession and Nutation, assuming the earth to have been originally 

 fluid. By William Hopkins, M.A., F.R.S., ^c. 



The mathematical investigation is intended to appear in the Trans- 

 actions of the Royal Society. 



Notice of certain Analytic Theorems. By Charles Blackburn, M.A. 



Remarks on Dr. Wollaston's argument respecting the infinite Divisibility 

 of Matter, drawn from the finite Fjxtent of the Atmosphere. By the 

 Rev. Wm. Whewell, F.R.S. 



He observed, that Dr. Wollaston had proceeded on this supposition : 

 That if the extent of the earth's atmosphere be finite, air must consist of 

 indivisible atoms ; since, as Dr. Wollaston assumed, the only way in which 

 we can conceive an upper surface of the atmosphere is, by conceiving an 

 upper stratum of atoms, the weight of which, acting downwards, is ba- 

 lanced by the repulsive force of the inferior strata acting upwards. Mr. 

 Whewell maintained, that such a mode of conception was altogether 

 arbitrary, and the argument founded upon it quite baseless ; for if we 

 investigate the relation between the height of any point in the atmo- 

 sphere, and the density of the air at that point, upon the supposition 

 that the compressing force is as the nth. power of the density, we find 

 that the density vanishes at a finite height whenever n is greater than 

 unity. Therefore, though the atmosphere do not consist of indivisible 

 particles, it will still have a finite surface. In fact, the finite surface of 

 the atmosphere no more proves the atomic constitution of air, than the 

 finite surface of water, in a vessel, proves the atomic constitution of 

 water. But it will still be asked, liow then is the highest stratum of 

 air supported ? To which the answer is, that there is no highest stra- 

 tum of definite thickness. Supposing the atmosphere finite, every 

 upper stratum of air bounded by the upper surface of the atmosphere, 

 has the upper part of that stratum supported by the lower ; and how- 

 ever thin the stratum be, it has still an upper and a lower part which 

 have this relation to each other. The question. What supports the 

 uppermost stratum of the atmosphere ? is of the same kind as the 

 question formerly discussed by writers on mechanics, What is the 

 velocity with which a body begins to fall ? 



