BEGINNINGS OF MODERN MATHEMATICAL SCIENCE 287 



with air : extreme minuteness, extreme hardness, extreme elas- 

 ticity. On this basis he worked out a consistent theory for re- 

 flection and refraction. His discussion of the newly discovered 

 phenomenon of double refraction in Iceland spar has been char- 

 acterized as an "unsurpassed example of the combination of ex- 

 perimental investigation and acute analysis." The attendant 

 phenomenon of polarisation did not escape him, but his theory 

 of wave motion was not sufficiently developed to enable him to 

 explain the matter adequately. 



In 1673 Huygens published his great work on the pendulum 

 (Horologiwn oscillatorium sive de motu pendulorum) , displaying 

 wonderful skill in his geometrical treatment of the mechanical 

 problems involved. The use of wheel mechanisms with weights 

 for measuring time had been more or less familiar for several cen- 

 turies, but no effective means for regulating this motion had 

 been devised. Galileo, for example, observing the regularity of 

 pendulum vibrations, had depended on repeated impulses by 

 hand to maintain the motion. Huygens first made the fortunate 

 combination of the two elements, without however inventing the 

 modern escapement. He studied the cycloidal pendulum for 

 which the time of an oscillation would be independent of the 

 amplitude and made precise determinations of the length of the 

 seconds-pendulum at Paris and the corresponding value of the im- 

 portant constant g. The most remarkable achievement in his 

 treatise on the pendulum is the correct analysis of the compound 

 pendulum based on the definition : 



The centre of oscillation of any figure whatever is that point in the 

 line of gravity, whose distance from the point of suspension is the 

 same as the length of the simple pendulum having the same time of 

 vibration as the figure. 



In the course of the discussion he formulates the important law, 

 afterwards somewhat generalized by others : 



Whenever any heavy bodies are set in motion under the action of 

 their own weight, their common centre of gravity cannot rise higher 

 than it was at the beginning of the motion. 



