INC 



INC 



it was repealed in April, 1802, and the 

 charges upon it transferred to the Con- 

 volidated Fund. 



In 1803 the income tax was revived, 

 with some alterations in the mode of col- 

 lecting it, under the title of the property 

 tax: the rate at which it was now im- 

 posed was 5 per cent, on all incomes 

 above 1501. per annum, and lesser pro- 

 portions on incomes between that amount 

 and 601. per annum. In 1805 it was in- 

 creased to 6 per cent.; and in 1806 it 

 was raised to the original rate at which it 

 had been imposed, or 10 per cent, while 

 the scale of lesser rates was made to com- 

 prehend all incomes amounting to 50/. per 

 annum. By this means, and by deducting 

 the tax on the dividends of the public 

 funds at the Bank, and abolishing most of 

 the former abatements and exemptions, 

 the sum raised by it has been consider- 

 ably augmented, the estimated produce 

 being as follows : 



1804 at Is. in the pound L. 4,650,000 



1805 at Is. 3d. ditto 5,937,500 



1806 at 2s ditto 11,500,000 



An income tax, if it could be so regu- 

 lated as to bear a just proportion to the 

 i different modes in which the incomes of 

 individuals arise, and did not extend to 

 I such amounts of income as are absolutely 

 i necessary for subsistence, would become 

 the most equitable, as well as the most 

 j productive mode of taxation. 



INCOMMENSURABLE, a term in 

 ) geometry, used where two lines, when 

 i compared to each other, have no common 

 j measure, how small soever, that will ex- 

 | actly measure them both. And in gene- 

 I ral two quantities are said to be incom- 

 i mensurable, when no third quantity can 

 be found that is an aliquot part of both. 

 Such are the diagonal and side of a square; 

 for though each of those lines have infi- 

 nite aliquot parts, as the half, the third, 

 &c. yet not any part of the one, be it ever 

 so little, can possibty measure the other, 

 as is demonstrated in prop. 117. lib. x. of 

 Euclid. 



INCOMMENSURABLE numbers, are such as 

 have no common divisor that will divide 

 them both equally. 



INCOMPLETE, in botany, a term used 

 to denote the sixteenth class of the Lin- 

 naen " methodus calycina," consisting of 

 plants whose flowers want either the ca- 

 lyx or petals. 



INCORPORATION, power of. To the 

 erection of any corporation the King's 

 consent is necessary, either impliedly or 

 expressly given : the King's implied con- 



sent is to be found in corporations which 

 exist by force of the common law, to which 

 the former kings are supposed to have 

 given their concurrence ; of this sort are 

 ail bishops, parsons, vicars, churchwar- 

 dens, and some others, who, by common 

 law, have ever been held to have been 

 corporations by virtue of their office. 

 Another method of implied consent is 

 with regard to all corporations by pre- 

 scription ; such as the city of London, 

 and many others, which have existed as 

 corporations for time immemorial; for 

 though the members thereof can show no 

 legal charter of incorporation, yet, in ca. 

 ses of such high antiquity, the law pre- 

 sumes there once was one, and that, by 

 variety of accidents, which a length of 

 time may produce, the charter is lost or 

 destroyed. The methods by which the 

 King's consent is expressly given are 

 either by act of parliament or charter ; 

 but the immediate creative act is usually 

 performed by the King alone, in virtue of 

 his royal prerogative. See further, JOINT 

 STOCK. 



INCREMENT, is the small increase of 

 a variable quantity. Sir Isaac Newton 

 calls these increases" moments," and ob- 

 serves, tkat they are proportional to the 

 velocity or rate of increase of the flowing 

 or variable quantities, in an indefinitely 

 small time. The notation of increment is 

 different by different authors. The method 

 of increments is a branch of analytics, in 

 which a calculus is founded on the proper- 

 ties of successive values of variable quan- 

 tities, and their differences, or increments. 

 It is nearly allied to the doctrine of 

 fluxions, and, in truth, arises out of it. 

 Of the latter the great Newton was the 

 inventor ; of the former we have different 

 treatises by Dr. Taylor, Mr. Emerson, and 

 others. We shall give Mr. Emerson's 

 observations on the distinction between 

 the method of increments and fluxions. 

 " From the method of increments," he 

 says, "the principal foundation of the 

 method of fluxions may be easily derived; 

 for, as in the method of increments, the 

 increment may be of any magnitude, so 

 in the method of fluxions it must be sup- 

 posed infinitely small; whence all preced- 

 ing and successive values of the variable 

 quantity will be equal, from which equa- 

 lity the rules for performing the principal 

 operations of fluxions are immediately 

 deduced. That I may give the reader,** 

 continues he, " a more perfect idea ofthe 

 nature of this method : suppose the ab- 

 scissa of a curve be divided into any num- 

 ber of equal parts, each part of which is 

 called the increment ofthe abscissa, and 



