MathejnatiCs. 36t 



Besides these may be enumerated the tables of 

 Logarithms, ot Sines, Secants, and Tangents, of 

 Difference of Latitude and Departure, of Meridio- 

 nal Points, of Loxodromic or Rliunib Lines, all of 

 which, and many more, have been brought to a 

 degree of perfection, during this period, which 

 was never before known. The tables more parti- 

 cularly entitled to honourable mention are those of 

 Sherwtn, Sharpe, Gardner, and Taylor, of 

 Great-Britain ; of Vega, of Germany ; and of J am- 

 BERT, Callet, and De Lalande, of France. 



To give an account, in detail, of the various in- 

 ventions and improvements which have taken place 

 with respect to Mathematical Listruments, during 

 the last age, would exceed the limits assigned to 

 the present review. Some of these have been al- 

 ready mentioned in another place; and many 

 more will readily occur to every reader, whose 

 mind is conversant with objects of this nature. It 

 is sufficient to say that they are numerous and 

 important. The accuracy of construction, the 

 elegance of workmanship, and the ease and expe- 

 dition of manufacture which modern artists have 

 attained, are equally wonderful, and honourable 

 to the century under consideration. 



The science of mathematics has been but little 

 cultivated in the United States during the period 

 under review. Our country, indeed, has been by 

 no means deficient in the production of mathe- 

 matical genius; but the state of society, and the 

 particular situation of most of those who might 

 have distinguished themselves in this department 

 of knowledge, have prevented that devotedness 

 to the higher branches of mathematics which is 

 necessary to the attainment of excellence, or to 

 accomplish improvements. Still, however, some 

 small productions of this kind, occasionally laid 

 before the public in the Transactions (jio\ix\c'dxuQ(l 



