X PREFACE. 



investigation of the resistance to be overcome by a wheel or roller ? 

 and an estimation of the ultimate pressure produced by a blow. 



In the hydraulic and optical part, may be enumerated an over- 

 flowing lamp ; a simplification of the rules for finding the velocity of 

 running water ; remarks on the application of force to hydraulic ma- 

 chines ; a mode of letting out air from water pipes ; an analysis of 

 the human voice; and some arrangements for^olar microscopes, and 

 for other optical instruments of a similar nature. 



In the astronomical and physical division of the work, will be found 

 a general rule for determining the correction on account of aberration ; 

 a comparison of observations on the figure of the earth ; a table of 

 the order of electrical excitation ; a chart of the variation of the com- 

 pass, and of the trade winds ; formulae for finding the heat of summer 

 and winter ; remarks on the theory of the winds ; and a comparative 

 table of all the mechanical properties of a variety of natural bodies. 



A few of these subjects have been more fully discussed in the miscel- 

 laneous papers, which have already been published, in the Philosophi- 

 cal Transactions and elsewhere, and which are now reprinted with cor- 

 rections and additions ; others are summarily investigated in the ma- 

 thematical elements, which form a part of the second volume, or in 

 the remarks, which are inserted, in their proper places, iatlie catalogue 

 of references. 



The arrangement of the whole work is probably dififerent in many 

 respects from any other that has yet been adopted ; the extent of the 

 subjects, which have been admitted, rendered it necessary to preserve 

 a very strict attention to a methodical and uniform system ; and it is 

 presumed, that this arrangement will be considered as in itself of some- 



