46 DISSERTATION SECOND. [part t». 



been the first writer who, in his Mechanica, published in 

 1669, founded an entire system of statics on the principle 

 of Galileo, or the equality of the opposite momenta. The 

 proposition, however, was first enunciated in its full generali- 

 ty, and with perfect precision, 1 by John Bernoulli, in a letter 

 to Varignon, so late as the year 1717. Varignon inserted 

 this letter at the end of the second edition of his Projet tfune. 

 Kouvelle Mecanique, which was not published till 1725. The 

 first edition of the same book appeared in 1687, and had the 

 merit of deriving the whole theory of the equilibrium of the 

 mechanical powers, from the single principle of the compo- 

 sition of forces. At first sight, there appear in mechanics 

 two' independent principles of equilibrium, that of the lever, 

 or of equal and opposite momenta, and that of the composi- 

 tion of forces. To show that these coincide, and that the 

 one may be deduced from the other, is, therefore, doing a 

 service to science, and this the ingenious author just nam- 

 ed accomplished by help of the property of the parallelo- 

 gram, which he seems to have been the first who demon- 

 strated. 



The Principia Mathematica of Newton, published also in 

 1687, marks a great era in the history of human knowledge, 

 and had the merit of effecting an almost entire revolution in 

 mechanics, by giving new powers and a new direction to its 



1 The principle of Virtual Velocities may be thus enunciated : 

 If a system of bodies be in a state of equilibrium, inconsequence 

 of the action of any forces whatever, on certain points in the 

 system ; then were the equilibrium to be for a moment destroy- 

 ed, the small space moved over by each of these points will ex- 

 press the virtual velocity of the power applied to it, and if each 

 force be multiplied into its virtual velocity, the sum of all the 

 products where the velocities are in the same direction, will be 

 equal to the sum of all tbose in wbich they are in the opposite. 



The distinction between actual and virtual velocities was first 

 made by Bernoulli, and is very essential to thinking as well 

 as to speaking with accuracy on the nature of equilibriums. 



