x AUTHOR'S PREFACE. 



eligible proportions of wheels and pinions ; remarks on the friction of 

 wheel work, and of balances ; a mode of finding the form of a tooth for 

 impelling a pallet without friction ; a chronometer for measuring minute 

 portions of time ; a clock scapement ; a calculation of the effect of tem- 

 perature on steel springs ; an easy determination of the best line of 

 draught for a carriage ; an investigation of the resistance to be overcome 

 by a wheel or roller ; and an estimation of the ultimate pressure pro- 

 duced by a blow. 



In the hydraulic and optical part, may be enumerated an overflowing 

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

 water ; remarks on the application of force to hydraulic machines ; a 

 mode of letting out air from water pipes ; an analysis of the human 

 voice ; and some arrangements for solar 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 compass, 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 Philosophical 

 Transactions and elsewhere, and which are now reprinted with corrections 

 and additions ; others are summarily investigated in the mathematical 

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

 which are inserted, in their proper places, in the catalogue of references. 



The arrangement of the whole work is probably different 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 value, espe- 

 cially in a work calculated to serve as a key, by means of which, access 

 may be obtained to all the widely scattered treasures of science ; and which 

 will enable those, who are desirous of extending their researches in any 

 particular department, to obtain expeditiously all the information that 

 books can afford them. 



It will not be thought surprising that the execution of this plan, allow- 

 ing for some professional engagements of a different kind, and for a 

 variety of accidental interruptions, should have occupied more than three 

 years, from the resignation of the professorship to the publication of the 

 work. Some part of it is in its nature incapable of permanent perfection, 

 since the catalogue must require to be continually extended by the 

 enumeration of new publications; and it might perhaps be desirable that 

 an appendix should be added to it, at least every ten years ; but the 

 lectures themselves may be expected to remain tolerably commensurate 

 to the state of the sciences for a much longer period ; since, in investiga- 

 tions so intimately connected with mathematical principles, the essential 



