IRR 



IRR 



may be truly in the centre of the wheel. 

 Fig 1 . 2. is a section of the two flasks when 

 put together ; but the core is not put in : 

 1 1 are the holes for the metal, and g hik 

 the hollow cavity to receive it. 



The iron is melted in a furnace, and 

 brought from it in a ladle (fig-. 11) which 

 has three handles, and is carried by two 

 men, the forked handle, M, giving a pur- 

 chase to the man holding it, to turn over 

 the ladle to deliver its contents. If the 

 work is very small, the metal is conveyed 

 to the flasks in common ladles. 



The more intricate cases of iron-found' 

 ery, as the casting of cylinders for steam 

 engines, crooked pipes with various pas- 

 sages, &c. are cast in moulds formed of 

 loam or clay, and are done nearly in the 

 same manner as the moulding of plaster 

 casts from busts, &c. but our limits will not 

 allow us to describe these curious branch- 

 es of the founder's art. 



1ROXY, in rhetoric, is when a person 

 speaks contrary to his thoughts, in order 

 to add force to his discourse. 



IRRATIONAL, an appellation given to 

 surd numbers and quantities. See SURD. 



IRREDUCIBLE case, in algebra, is 

 used for that case of cubic equations, 

 where the root, according to Cardan's 

 rule, appears under an impossible or 

 imaginary form, and yet is real. Thus, 

 in the equation, ,r3 90 x 100 = 0, 

 the root, according to Cardan's rule, 



will be a- = \/ 50 -j- </ 24oOU -f- 



\/ 50 ^/ 24500, which is an impos- 

 sible expression, and yet one root is equal 

 to 10 ; and the other two roots of the 

 equation are also real. Algebraists, for 

 two centuries, have in vain endeavoured 

 to resolve this case, and bring it under a 

 real form ; and the question is not less fa- 

 mous among them than the squaring 1 of 

 the circle is among geometers. See 

 EQ.UATIOX. 



It is to be observed, that as, in some 

 other cases of cubic equations, the value 

 of the root, though rational, is found under 

 an irrational or surd form ; because the 

 root in this case is compounded of two 

 equal surds with contrary signs, which 

 destroy eacli other ; as if "r =5 + ^/5 

 + 5 v' 5 J tllen x = 10 ; in like man- 

 aier, in the irreducible case, when the root 

 is rational, there are two equal imaginary 

 quantities, with contrary signs, joined 

 to real ^quantities ; so that the imaginary 

 quantities destroy each other. Thus the 

 expression : _ 



V 50 -f \/~= 



5 ; and 

 3/ 50 -</-- 24500 = 5 -^-5. But 



5 + v/ 5 + 5 Y/ 5 = 10 = x, the 

 root of the proposed equation. 



Dr. Wallis seems to have intended to 

 show, that there is no case of cubic equa- 

 tions irreducible, or impracticable, as he 

 calls it, notwithstanding the common opi- 

 nion to the contrary. 



Thus in the equation r3 63 r = 162, 

 where the value of the root, according to 

 Cardan's rule, is, r =*/ 81 -f Y/ 2700 

 + ^/8l ^/ 2700, the doctor says, 

 that the cubic root of 81 -f v/ 2700, 

 may be extracted by another impossible 

 binomial, viz. by ~ -f- ^ \/ ; ^"d in the 

 same manner, that the cubic root of 81 

 Y/ 2700 may be extracted, and is equal 

 to -| 3 \/ 5 ; from whence he infers, 

 that + is ^/ 3 -f | 1 Y/ 3 = 9, 

 is one of the roots of the equation pro- 

 posed. And this is true : but those who 

 will consult his algebra, p. 190, 191, will 

 find that the rule he gives is nothing but 

 a trial, both in determining that part of 

 the root which is without a radical sign, 

 and that part which is within : and if the 

 original equation had been such as to have 

 its roots irrational, his trial would never 

 have succeeded. Besides, it is certain, 

 that the extracting the cube root of 81 

 -f- Y/ 2700 is of the same degree of 

 difficulty, as the extracting the root of the 

 original equation r3 63 r = 162 ; and 

 that both require the tri-section of an an- 

 gle for a perfect solution. 



IRREGULAR, in grammar, such in- 

 flections of words as vary from the origi- 

 nal rules : thus we say, irregular nouns, 

 irregular verbs, &c. 



IRRIGATION is the art of conducting 

 water at pleasure over levels or inclined 

 planes, in such manner that the whole 

 may receive the benefit of partial immer- 

 sion ; whereby the surface may be duly 

 supplied with moisture, and the vegetable 

 production^ intended to be encouraged, 

 should be enabled to put forth abun- 

 dantly, and to yield a good crop. Irriga- 

 tion is with us rather a novel practice, 

 but was well understood by the ancients, 

 and has been in use among the Chinese 

 up to the earliest da\es of their records. 

 In Hindostan, the whole of the rubbee, or 

 small-grain crop, is artificially watered ; 

 the grain being deposited in October, 

 while the ground remains moist, after the 

 heavy rains which had fallen for months 

 previously to the operations of tillage; so 

 that the seed speedily germinates. But 

 the perfect drought atte'ndant on the five 

 successive months, would infallibly destroy 

 the promising verdure, were it not tlia^ 

 the peasants divide their lands into small 





