IMP 



cure the payment of heavy duties on al- 

 most every article of trade will admit. 

 Total official value of the imports of 

 Great Britain in the year 1800. 



L. s. d. 



Port of London . 18,843,172 2 10 

 The Out Ports . . 9,514,642 11 20 



England 28,357,814 14 8 



Scotland ..... 2,212,790 11 8 



30,570,605 6 4 



In 1801 L 32,795,556 



1802 31,441,318 



1803 27,992,464 



1804 92,201,490 



1805 30,344,628 



1806 28,835,907 



1807 29,556,330 



These sums are the official value of 

 goods imported, which is very different 

 from the real value ; as an instance, which 

 may serve for every case, the official va- 

 lue of the imports for 1807, <!9,556,330Z. ; 

 but the real value, according to the ave- 

 rage of the last three years, is 53,500,990^. 



1MPOSTHUME. a collection of matter 

 or pus in any part of the body, either ow- 

 ing to previous.inflammation of the part, 

 -or a translation of it from some other 

 part. 



IMPOSSIBLE roots, in algebra. To 

 discover how many impossible roots are 

 contained in any proposed equation, Sir 

 Isaac Newton gave this rule in his alge- 

 bra, viz. Constitute a series of fractions, 

 whose denominators are the series of na- 

 tural numbers, 1, 2, 3, 4, 5, &c. continued 

 to the number showing the index or expo- 

 nent of the highest term of the equations, 

 and their numerators the same series of 

 numbers m the contrary order ; and di- 

 vide each' of these fractions by that next 

 before it, and place the resulting quo- 

 tients over the intermediate terms of the 

 equation; then, under each of the inter- 

 mediate terms, if its square multiplied by 

 the fraction over it be greater than the 

 product of the terms on each side of it, 

 place the sign -}- ; but if not, the sign 

 ; and under the first and last term 

 place the sign +. Then will the equa- 

 tion have as many imaginary roots as 

 there are changes of the underwritten 

 signs from + to , and from to -{- So 

 for the equation x? 4T 1 -+- 4x 6=0, 

 the series of fractions is j* , |. ? * : then the 

 pecond, divided by the first, gives, .| or -|, 



IMP 



and the third divided by the second gives 

 ^ also ; hence these quotients, placed 

 over the intermediate terms, the whole 

 will stand thus : 



i 



Now because the square of the second 

 term, multiplied by its superscribed frac- 

 tion, is I* x*, which is greater than 4 x*, 

 the product of the two adjacent terms, 

 therefore the sign + is set below the se- 

 cond term; and because the square of 

 the third term, multiplied by its over 

 written fraction, is \* x 1 , which is less 

 than 24;r l , the product of the terms on 

 each side of it ; therefore the sign is 

 placed under that term ; also the sign -|- is 

 set under the first and last terms. Hence 

 the two changes of the underwritten 



signs -4- H H- tne one fr m + to 



and the other from to -}-, show that the 

 given equation has two impossible roots. 

 When two or more terms are wanting 

 together, under the place of the first of 

 the deficient terms write the sign , un- 

 der the second the sign -{-, under the 

 third , and so on, always varying the 

 signs, except that under the last of the 

 deficient terms must always be set the 

 sign -J-, when the adjacent terms on both 

 sides of the deficient terms have contrary 

 signs. As in the equation, 



4- +-+.- + 



which has four imaginary roots. 



IMPOSTS, in architecture, the capi- 

 tals of pillars, or pilasters, which support 

 arches. An impost, sometimes called chap- 

 trel, is a sort of a plinth, or little corniche, 

 which crowns a pier, and supports the first 

 stone whence an arch or vault commences. 

 The imposts are conformable to their pro- 

 per orders. The Tuscan has only a 

 plinth ; the Doric has two faces crowned; 

 the Ionic, a larmier, or crown over the 

 two faces, and its mouldings may be carv- 

 ed ; the Corinthian and Composite have 

 a larmier, frieze, and other mouldings. 

 See ARCHITECTURE. 



IMPOTENCY, in the ecclesiastical 

 law, signifies an inability of generation, 

 or propagating the species, which is a 

 cause of divorce a vinculo matrimonii, as 

 being merely void, and therefore needs 

 only a sentence declaratory of its being so. 



IMPRESSING men. The power of 

 impressing seamen for the sea-service, 

 by the King's commission, has been a 

 matter of some dispute, and submitted to 

 with great reluctance, though it has very 

 clearly and learnedly been shown by Sir 



