PREFACE, 



THE substance of the following -pages has already ap- 

 peared, partly in the Philosophical Magazine, 1871, 1872, 

 and the Quarterly Journal of Mathematics, 1872, and 

 partly in Hermathena, 1882. Hitherto correct statements 

 about the Tides have been confined to treatises which 

 employ the resources of the higher mathematics. Other 

 works almost without exception* repeat such erroneous 

 statements as that the place of high water without 

 friction would be under the moon, and that high water 

 is retarded by friction. No apology then is needed for 

 the publication, in a more accessible form, of the present 

 Essay, in which the fundamental theorems are deduced 

 from elementary physical principles without the use of 

 mathematics, except for quantitative calculations. The 

 problem of the influence of the Tides on the length of 

 the day is discussed in a similar method. 



* The only exception with which I am acquainted is Stubbs' edition of 

 Brinkley's Astronomy, in which the reasoning of this Essay is adopted. 



