EXP 



EXP 



tio of 1 to 9 ; and since, according to Eu- 

 clid, if three quantities be proportional, 

 the ratio of the first to the third is said 

 to be the duplicate of the ratio of the first 

 to the second, and of the second to the 

 third ; therefore, according to this, ^ must 

 be the double of ^, which is very false. 

 But it is well known, the logarithm of the 

 ratio of 1 to 9, that is, the logarithm of 9, 

 is the double of the ratio of 1 to 3, or 3 to 

 9, that is, the logarithm of 3. From 

 whence it appears that logarithms are 

 more properly the exponents of ratios, 

 th*n numerical quotients ; and Dr. Halley, 

 Mr. Cotes, and others, are of the same 

 opinion. 



EXPONENT, is also used in arithmetic, 

 in the same sense as index or loga- 

 rithm. 



EXPONENTIAL curve, is that whose 

 nature is expressed by an exponential 

 equation. The area of any exponential 

 curve, whose nature is expressed by this 

 exponential equation x x = y (making 



1 -j- v = x will be v 1 



'0.1.2 



u.1.2.3 

 1 



0.1.2.3.4' ''0.1.2.3.4.5 0.1.2.3.4.0.6, 

 v 6 , &.c. 



EXPONENTIAL equation, is that where- 

 in there is an exponential quantity. See 

 the next article. 



EXPONENTIAL quantity, is a quantity 

 whose power is a variable quantity, as 

 x* , u x . Exponential quantities are of 

 several degrees and orders, according as 

 the exponents themselves are more or 

 less involved. If the exponent be a sim- 

 ple quantity, as zy, it is called an expo- 

 nential of the first or lowest degree ; but 

 when the exponent itself is an exponen- 

 tial of the first degree, as zy x , it is called 

 an exponential of the second degree. In 

 like manner, if the exponent itself be an 

 exponential of the second degree, as xyx, 

 it is called an exponential of the third de- 

 gree, &c. 



EXPORTATION, the act of sending 

 goods out of one country into another. 

 In modern times it has been the principal 

 object of commercial policy, in almost 

 every country, to encourage exportation, 

 except with respect to a few particular 

 articles ; the export of manufactured 

 goods has been promoted, with a view of 

 encouraging the internal industry of the 

 country, and the export of foreign pro- 

 duce, as a means of drawing wealth from 

 other countries by the profits of the car- 

 rying trade. The excess of the value of 

 goods exported, beyond that of the ira- 



ports has usually been considered as * 

 criterion of the profits which a country 

 derives from foreign trade ; but this is a 

 very fallacious mode of determining a 

 point of great importance ; advantageous 

 foreign trade mig'u long txist, even if 

 the imports constantly exceeded the value 

 of the exports. Tiie laws in force relat- 

 ing to exportation, consist principally of 

 prohibitory or restrictive regulations, re- 

 specting bullion, corn, wool, machinery, 

 and tools used in various branches oi 

 manufactures, the exportation of which, 

 it is thought, might diminish the neces- 

 sary supply of provisions for the consump- 

 tion of the country, or enable foreigners 

 to rival valuable branches of its manu- 

 factures. Tne acts relative to the expor- 

 tation of wool prohibit the exportation, 

 not only of the article itself, but aiso of 

 live sheep, rams, or lambs, from Great 

 Britain, Ireland, Jersey, Guernsey, Akler- 

 ney, Sark, or Man, on penalty of the for- 

 feiture thereof, and of the ships convey- 

 ing the same ; also 31 for ev. ry sheep, 

 &.c. and the offender to suffer three 

 months solitary imprisonment; for a se- 

 cond offence 51. per sheep, &c. and six 

 months imprisonment ; except wether 

 slieep for ships' use only, put on board 

 by licence of the port officer of the cus- 

 toms. A limited quant ivy of wool is, how- 

 ever, permitted to be exported from the 

 port of Southampton to Jersey, Guernsey, 

 Alderney, and Sark. The duties on ex- 

 portation, payable in Great Britain and 

 Ireland, which were formerly the prin- 

 cipal branch of the revenue derived from 

 foreign trade, are now of small amount, 

 in comparison with the duties payable on 

 goods brought into the country. See 

 CUSTOMS. 



EXPRESSED oil. See OIL. 



EXPRESSION, in chemistry, or phar- 

 macy, denotes the act of expressing out 

 the juices or oils of vegetables, which is 

 one of the three ways of obtaining them ; 

 the other two being by infusion and de- 

 coction. The hard fruits require to be 

 well bruised previously to expression, but 

 herbs are only to be moderately bruised. 

 They are then to be included in a hair 

 bag, and pressed between wooden plates 

 in the common screw press, till the juice 

 ceases to run. The expression of oils is 

 performed nearly in the same manner as 

 that of juices, only iron plates are to be 

 used instead of wooden ones. The in- 

 sipid oils of all unctuous seeds are ob- 

 tained uninjured by this operation, if per- 

 formed without the aid of heat, which 



