INTRODUCTION. 



THIS small volume is intended, as its title page imports, partly 

 as a Manual for the scientific man, to aid him in his researches, 

 when, from his distance from home, or other circumstances, he 

 is precluded from having access to more extended and elaborate 

 works ; and partly as a convenient appendage to the table of 

 the general reader, for purposes of occasional reference ; while 

 to the Student it will supply the place of a syllabus, and fur- 

 nish him with formulae for the solution of problems in many 

 useful branches of mixed Mathematics. 



With respect to its plan, the reader, on turning to any 

 article, will usually find entered first the Propositions or 

 Formulae applicable to it, illustrated, if necessary, by ex- 

 amples ; to which are appended, such practical results and 

 tables as the subject appeared to require, or the limits of the 

 book to admit of. 



The Propositions are very rarely accompanied by proofs ; nor 

 is any explanation given of the various terms employed, further 

 than what is necessary to a due understanding of the several 

 symbols introduced. The book professing merely to supply a 

 combination of facts, calculated to aid the memory, or exercise 

 the ingenuity, of the reader, any attempt at elementary instruc- 

 tion would have been altogether inconsistent with its scope and 

 principle. 



Most of the articles have been compiled and abridged from 

 original sources, as will appear from referring to their several 



