474 Mr. R. F. Muirhead on the Laws of Motion. 



validity ot its processes and results, it may appear somewhat 

 strange that much difficulty has been found in stating its 

 principles in a satisfactory form. 



In the preface to the second edition of Tait and Steele's 

 1 Dynamics of a Particle ' we read (referring to the chapter 

 on the Laws of Motion) : — " These five pages, faulty and even 

 erroneous as I have since seen them to be, cost me almost as 

 much labour and thought as the utterly disproportionate 

 remainder of my contributions to the volume ; and I cannot 

 but ascribe this result in part, at least, to the vicious system 

 of the present day, which ignores Newton's Third Law, &g." 



And when we read Clerk Maxwell's notice of the 2nd 

 edition of Thomson and Tait's treatise in ' Nature/ * we feel 

 that the reform introduced by Thomson and Tait, in " return- 

 ing to Newton," still leaves something to be desired. This 

 feeling is strengthened when we learn from the late Prof. 

 Clifford f , that " no mathematician can attach any meaning 

 to the language about force, mass, inertia, &c. used in current 

 text-books of Mechanics/' 



It will then be worth while to clear up the logic of the 

 science, and, if possible, to state the laws of motion in a form 

 that shall be free from all ambiguity and confusion. 



Let us cast a brief and partial glance over the history of 

 the development of dynamical first principles. 



Though one region of the science of Dynamics, namely 

 Statics, was cultivated by the ancients, it was left for Galileo 

 Galilei to become the pioneer of dynamical science in its full 

 extent. 



Before Galileo, the idea of force as something measurable 

 was attained to. The causes tending to disturb rest were 

 perceived to have a common kind of effect, so that for the 

 purposes of Statics they could be represented by the tension 

 of cords produced by suspending from them weights of 

 determinate magnitude. Galileo paved the way for the intro- 

 duction of the kinetic idea of force, i. e. that of the cause of 

 the acceleration of the motion of bodies. It is noteworthy, 

 however, that he approached the subject from a kinematical 

 standpoint. In his { Dialogues/ he treats of the science of 

 " Local Motion/' not of the science of Force ; and in his 

 investigations on the motion of Projectiles in that work, his 

 aim is to describe the properties of their motion, not to 

 speculate on causes. 



Another stage was reached when Newton published the 



* 'Nature/ vol. xx. p. 213,//. 

 t Ibid. vol. xxii. June lOtn. 



