NOTES ON STATICS. 231 



In every occupation wbich admits of the advantageous employment 

 of both hands, the left-handed person has this advantage that, starting 

 as he does with a natural facility in the use of the one hand, many 

 circumstances compel him to the education of the other, and thus he 

 becomes practically ambidextre, or not unfrequently learns to delegate 

 special operations to each hand, as those for which experience and 

 training have best adapted it. Nevertheless the instinctive preference 

 is never eradicated. In every sudden and unpremeditated action the 

 prompt use of the left hand shows that there remains, after the utmost 

 educational training, some inherent impulse, resulting in a greater 

 aptitude in the one hand than the other. 



NOTES ON STATICS. 



BY JAMES LOUDON, M.A., 



MatJiamatical Tutor and Dean, University College, Toronto. 



The following Greometrical proofs of some propositions in Statics 

 were devised by me in the year 1868 : 



1. Let OA r= r be any line; P^, F.^, ... the forces under which a 

 system is kept at rest; 0^, O.^, ... the angles between their directions 

 and OA. 



Then forming a closed polygon with the lines representing the 

 forces, and projecting the sides on OA, we have 2'(Pcos 6) = 0, and 

 therefore S {Fr cos 0) = 0, that is, 



Pi . r cos ^1 + P, . r cos 6*2 + ... = 0. 



But r cos is the projection of OA on the line inclined to it at angle 6. 

 Wherefore, &c. 



2. Let the forces P^, F.y ...he ia equilibrium, or reducible to a single 

 resultant. 



Let pi be the perpendicular from on P^, d^ the perpendicular 

 from A on the plane of p^ and P^, &c. 



Then forming a closed polygon with the axes of the couples, and 

 projecting the sides on the line OA, we have F^ p^ cos 0^ -\- ... = 0. 

 But 3 =0A cos 0^, &o.; therefore Pi2>i^i+ •■• =0, or S {Fpd) = 0. 



