88 Smics.—.Metms cf Fluids, 



Mufchenbroek and mod of the philofophers of the prefent century have attributed 

 fcarcely any other fun£lion to the air than that of comprefTing the caloric or fuel in « 

 flate of combuftion, and blowing away the afhes. Chemiftry has lately proved what 

 Vinci had before diicerned, and Mayow and Hooke had fufpecled towards the end of the 

 laft century. 



VII. and Vlir. On Statics. — The author explains the theory of the oblique lever, the 

 inclined plane, and the general principle of virtual velocities in machines. 



Vinci and Galileo both obferved, that the defcent of heavy bodies is made more fpeedily 

 through an arc of a circle than by an inclined plane ; but their proofs are imperfect in cer- 

 tain rcfpe£ls. It has fince been dcmonftrated that the cycloid is the curve of quickeft de- 

 fcent. Neverthelefs, I find that there is a minimum of time of defcent in a circular arc, 

 which may be determined in a fynthetical method of confiderable fimplicity, by means of 

 the following theorem. 



An arc of a circle which does not. exceed 60° is a curve of fpeedier defcent than any 

 other curve which can be drawn within the fame arc : — and the arc of 90° is a curve of 

 fpeedier defcent than any other curve which can be drawn without the fame arc*. 



IX. Concerning water drawn from a canal. — The quantity of water which iflues from a 

 canal through a given aperture, may vary from many caufes. i. From the greater or lefs 

 height of the water of the canal above the aperture. 2. From the greater or lefs fwiftnefs 

 of the water along the fide or bank, in which the opening is made. 3. From the greater 

 or lefs convergence of the fides of the aperture. 4. The greater or lefs thicknefs of the 

 fide of the canal. 5. Whether the aperture be circular, fquare, triangular, or oblong. 

 6. Bccaufe the aperture is more or lefs obliquely fituated with regard to the bearing or 

 dire£lion of the fide. 7. Or more or lefs Inclined to the horizon. 8. Whether the opening 

 be in a convex or concave part of the bank. 9. Whether there be cavities or prominences 

 in the bed of the canal oppofite the aperture. 10. Whether the air do or do not infinuate 

 jtfelf into the current of water which iflues forth. 1 1. Whether the water at its emiflion 

 fall freely in the air, or is conducted away by an open trough, or by a pipe clofed all 

 round. 12. Whether this conducing pipe have a greater or lefs diameter with regard to 

 the quantity of water which defcends in the tube itfelf. 13. Whether the fame conduc- 

 ing pipe have a greater or lefs length in its defcent. And 14. Whether the bore of this 

 pipe be equal or rough, ftraight or curved. 



It muft be admitted here, as well as elfewhere, that De Vinci, though poflefled of a mind 

 fo powerful as to difcern the true caufes of natural phenomena, had not the advantage of 

 modern analyfis to afcertain and demonflrate the quantum of a£tion of thefe caufes. But, 

 on the other hand, it muft be allowed that hydraulics even in our time has not yet perfedly 

 and accurately determined all the laws according to which the fourteen circumftances 

 pointed out by Leonardo afFeft the quantity of water emitted through an aperture of a 

 given magnitude. 



X. Concerning circular eddies, or whirls of water.— The author marks the efFe<^ of the 

 inertia of bodies which produces a centrifugal force in curve-lined motions. He remarks that 

 the cavity produced in water by a whirling motion is leaft at the bottom, becaufe there the 



* For the demonftration I muft refer to the Effay, p. 19. N. 



o prcflure 



