PRESIDENTIAL ADDRESS, B.A., 1871. 149 



condensations and expositions of the branches of 

 science to which they relate. I cannot better 

 illustrate the two kinds of efficiency realised in 

 this department of the Association's work than 

 by referring to Cayley's " Report on Abstract 

 Dynamics " l and Sabine's " Report on Terrestrial 

 Magnetism" 2 (1838). 



To the great value of the former, personal 

 experience of benefit received enables me, and 

 gratitude impels me, to testify. In a few pages 

 full of precious matter, the generalised dynamical 

 equations of Lagrange, the great principle evolved 

 from Maupertuis' " least action " by Hamilton, and 

 the later developments and applications of the 

 Hamiltonian principle by other authors are de- 

 scribed by Cayley so suggestively that the reading 

 of thousands of quarto pages of papers scattered 

 through the Transactions of the various learned 

 Societies of Europe is rendered superfluous for 



1 "Report on the Recent Progress of Theoretical Dynamics, "by 

 A. Cayley (Report of the British A ssociation, 1857, p. i). 



- " Report on the Variations of the Magnetic Intensity observed at 

 different points of the Earth's Surface," by Major Sabine, F. R. S. 

 (forming' part of the seventh Report of the British Association}. 



