OF PRESSURE AND EQUILJBRIUM. 87 



forces according to the laws of motion, there can be no 

 question that the resulting motion is truly determined in 

 all cases, whatever may be its magnitude, nor can any 

 reason be given why it should be otherwise, when this 

 motion is evanescent, and the force becomes a pressure. 



Scholium 2. The proposition may be famiharly illus- 

 trated by a simple experiment ; we attach three weights 

 to as many threads, united in one point, and passing over 

 three pullies ; then by drawing any triangle, of which the 

 sides are in the directions of the threads, or in directions 

 parallel to them, we may always express the magnitude of 

 each weight by the length of the side of the triangle corres- 

 ponding to its thread. 



Scholium 3. The laws of pressure have however 

 been deduced by some of the most celebrated mathema- 

 ticians, independently of those of motion, from the prin- 

 ciple of the equality of the effects of equal causes; and 

 such a demonstration may be found in an improved form, 

 in the article Dynamics of the First Supplement of the 

 Encyclopaedia Britannica, contributed to that publication 

 by the late Professor Robison; but its steps are still tedious 

 and intricate. It will however be necessary, in conformity 

 with the plan of this work, to insert here the demonstra- 

 tion of Laplace, which is sufficiently conclusive, though 

 less simple than conld perhaps be desired: and it will be 

 convenient to premise some lemmas, which are but very 

 slightly connected with the immediate subjects of discus- 

 sion. Every lemma is indeed an interruption of systematic 

 order, and is inadmissible in a completely methodical trea- 

 tise; but in following the steps of another author, this 

 interruption may sometimes become indispensable. 



