\OL. XXXV.] PHILOSOPHICAL TRANSACTIONS. 205 



instead of being proportional, would be more than in proportion to their causes. 

 Thus, the effect of a pressure of a column of any fluid, as water, g inches 

 high, instead of being but 9 times greater than that of 1 inch above the 

 orifice, will be no less than 27 times greater. For the velocity being at 

 this height triple, the quantity of matter in a given time will also be triple; 

 which last, multiplied by the square of the velocity, gives 1^ for the force 

 communicated by a pressure of 9 inches in altitude, while the force communi- 

 cated by the pressure of 1 inch, is but as 1. So that the moving forces pro- 

 duced will be as 27 to 1, while the causes producing these forces, are but as 9 

 to 1, i. e. three times too little for such a purpose. 



Thus again, if the velocities be as 1 and 4, the quantities of water issuing 

 out will be as 1 and 4 ; but the effects, or forces produced, according to the 

 new rule, will be as 1 and 64; though the pressures which communicate them 

 are only as the altitudes, which are as ] and 16. Whereas, to produce such 

 effects, the altitudes of the latter column ought to have been as 64, i. e. four 

 times greater than by experience it is found to be. 



Remark III. Mr. Eames observes, in the last place, that the common rule 

 of estimating the forces of moving bodies, by the quantities of matter multi- 

 plied by their velocities, is rather confirmed by these very experiments. For 

 then, according to the old maxim, effects are proportional to their causes, the 

 forces communicated will be as the forces communicating, or pressures. Thus, 

 let the altitude, and consequent pressure of any column of water, be 9 

 times greater than the altitude of another; then the velocity of every single 

 particle of water pressed out will be triple, and the number of particles issuing 

 out in a given time will likewise be triple; therefore the force resulting from 

 these two multiplied together, according to the common rule, will be g, pro- 

 portional to the pressure, as it ought to be. So again, if the altitude be 

 16 times greater, the velocity will be quadruple, and the number of the par- 

 ticles quadruple, and the force produced the product of these two, i. e. 1 6, still 

 proportional to the altitude, or pressure. 



And universally, the forces communicated, according to the old rule, are in 

 a ratio compounded of two others, one of the quantities of matter, and the 

 other of the velocities; the ratio of the velocities, by the experiments, is the 

 subduplicate ratio of the heights, and the ratio of the quantities of matter is, 

 by confession, likewise the subduplicate of the heights; therefore the com- 

 pound of these two is the ratio integra, or simple ratio of the heights, in which 

 ratio are the pressures themselves, which produce these moving forces; so that, 

 according to the common rule, the effects are always, as they ought to be, 

 proportional to their causes. 



