Demonstration of the Parallelogram of Forces. 223 



less of the grosser aether, in proportion of the finer, than in 

 the regions of the air ; and that yet the grosser aether in the 

 air affects the upper regions of the earth, and the finer aether 

 in the earth the lower regions of the air, in such a manner, 

 that from the top of the air to the surface of the earth, and 

 again from the surface of the earth to the centre thereof, the 

 aether is insensibly finer and finer. Imagine now any body 

 suspended in the air, or lying on the earth, and the aether 

 being by the hypothesis grosser in the pores, which are in the 

 upper parts of the body, than in those which are in its lower 

 parts, and that grosser aether being less apt to be lodged in 

 those pores than the finer aether below, it will endeavour to 

 get out and give way to the finer aether below, which cannot 

 be, without the bodies descending to make room above for it 

 to go out into. 



From this supposed gradual subtilty of the parts of aether 

 some things above might be further illustrated and made 

 more intelligible; but by what has been said, you will easily 

 discern whether in these conjectures there be any degree of 

 probability, which is all I aim at. For my own part, I have 

 so little fancy to things of this nature, that had not your en- 

 couragement moved me to it, I should never, I think, have 

 thus far set pen to paper about them. What is amiss, there- 

 fore, I hope you will the more easily pardon in 



Your most humble servant and honourer, 

 Cambridge, Feb. 28, 1678-9. ISAAC Newton. 



XXXVI. A New Analytical Demonstration of the "Paral- 

 lelogram of Forces" By Thomas Weddle, Esq., New- 

 castle-on-Tyne* '• 



HPHE following investigation of this fundamental proposi- 

 tion, whatever may be its defects, has at least one ad- 

 vantage — the most general case is discussed at once. In all 

 the analytical proofs that I have seen, a particular case only 

 is established analytically ; thus Laplace (Mecanique Celeste) 

 and Pontecoulant (Systeme du Monde) consider the forces to 

 act at right angles; and Poisson {Mecanique) first finds the 

 resultant of two equal forces, and afterwards thence deduces, 

 by geometrical considerations, that of any two forces. I have 

 here attempted to conduct the whole investigation analytically, 

 and to do so without first establishing a particular case. 

 I shall assume that the resultant of two equal forces bisects 



* Communicated by the Author. 



