VOL. XXXIV.] PHILOSOPHICAL TRANSACTIONS. 17 1 



direction, perpendicularly, and the other to move in three oblique directions, 

 and but one perpendicular. 



Let therefore the same body move always in the same directions; and, with 

 a small alteration, the argument used in this demonstration will be so far from 

 proving that side only of the question for which it was brought, that it will 

 equally serve to prove the truth of the other, namely, that the forces of the 

 same body moving with different velocities areas those velocities. Let therefore 

 the same body, instead df moving with 2 degrees of velocity, move with only 

 one, and in the same directions as above; only let the springs be capable of 

 destroying but half a degree of velocity in a perpendicular direction ; then by 

 the same steps of reasoning it will follow, that this body will now also bend 4 

 similar springs, before its force is spent; so that the same body moving with half 

 the velocities, and in the same directions as before, bends the same number of 

 springs; only now the springs make but half the resistance, that the springs in 

 the former case made; therefore the etFect in this case, according to our way of 

 estimating an effect, is only half the former effect; consequently the forces 

 producing these effects are as 2 to 1 ; but in this ratio are the velocities, witli 

 which the body moved in the two cases, therefore the forces are as the 

 velocities. 



Let the body move with 3 degrees of velocity, and it will bend 9 similar 

 springs, each destroying one degree of velocity in a perpendicular direction, 

 before the whole force is consumed. So also by the same way of arguing, it is 

 as certain, that if the same body move with one degree of velocity, it will bend 

 g similar springs, each destroying a third part of one degree of velocity in a 

 perpendicular direction, before its force is extinguished; so that still the effects, 

 or resistances overcome, in the same directions, are, according to our way of 

 computing, as 3 to 1 ; and so also their forces must be but in the same ratio 

 of 3 to 1, as were the velocities; consequently the forces are as the velocities. 



Since therefore this proof, drawn from the doctrine of composition and reso- 

 lution of forces, equally proves both sides of the question, it proves too much, 

 or in reality nothing at all ; and is therefore far from deserving the name of a 

 demonstration. 



Brevis Commentatio de Cobalto, Auctore f^iro Ctari.ssimo Joh. Henr. Linchio, 

 Lipsiensj, Acad. Ccesar. Leopold. Carolin. Nat. Curios, el Sac. Reg. Anglic. 

 Sodale. Lipsia-, mense Quintil. A. R. S. 172,6. N" 396, p. ig2. 



There is nothing in this account of Cobalt that is in the least degree interest- 

 ing at the present day, when the natural history, chemical properties and uses, 



z 2 



