THE author desires to record his gratitude to Mr. W. W. 

 EOUSE BALL, Fellow of Trinity College, Cambridge, and to 

 Professor W. McF. ORR, F.R.S., of the Royal College of Science 

 for Ireland ; these friends have read the proof-sheets, and have 

 made many helpful suggestions and criticisms. 



Thanks are also 'due to the BOARD OF TRINITY COLLEGE, 

 DUBLIN, for the financial assistance which made possible the 

 publication of the work. 



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