If A 



FRU 



area of the greater end 

 . lesser end 



h = height : then 



A + tf-f \/ A 



i T 1-4. 

 the solidity. 



The frustum of a globe or sphere is 

 any part thereof cut off by a plane, the 

 solid contents of which may be found by 

 this rule. To three times the square of 

 the semi-diameter of the base, add the 



FUE 



or oblique, and not only of the solids ge- 

 nerated from the conic'sections, but also 

 of all pyramids, cones, and in short of any __ 

 solid, whose parallel sections are similar 

 figures. 



FUCHSIA, in botany, so called in ho- 

 nour of Leonard Fuchs, a famous German 

 botanist, a genus of the Octandria Mono- 

 gynia class and order. Natural order of 

 Onagrx, Jussieu. Essential character : ca- 

 lyx one-leafed, coloured, bearing the co- 

 rolla, very large ; petals four, small ; ber- 



square of its height ; then multiplying r y inferior, four-celled, with many seeds, 

 that sum bv the height, and this product T] 



_. - heigh., 



multiplied by 5236, gives the solidity ot 

 the frustum. A frustum, or portion of 

 any solid, generated by the revolution of 

 any conic section upon its axis, and ter- 

 minated by any two parallel planes, may 

 be thus compared to a cylinder of the 

 same altitude, and whose base is equal 

 to the middle section of the frustum 

 made by a parallel plane. 1. The differ- 

 ence between such frustum and cylinder 

 is always the same in different parts of the 

 same or of similar solids, when the in- 

 clination of the planes to the axis and the 

 altitude of the frustum are given. 2. In 

 the parabolic conoid, this difference va- 

 nishes ; the frustum being always equal 

 to a cylinder of the same height, upon 

 the section of the conoid that bisects the 

 altitude of the frustum, and is parallel to 

 its bases. 3. In the sphere, the frustum 

 is always less than the cylinder, by one 

 fourth part of a right angled cone of the 

 same height with the frustum ; or by one 

 half of a sphere, of a diameter equal to 

 that height : and this difference is always 

 the same in all spheres whatever, when 

 the altitude of the frustum is given. 4. In 

 the cone, the frustum always exceeds the 

 cylinder, by one fourth part of the content 

 of a similar cone, that has the same height 

 with the frustum. 



As a general theorem : in the frustum 

 of any solid, generated by the revolution 

 of any conic section about its axis : if xo 

 the sum of the two ends be added four, 

 times the middle section, then the last 

 sum divided by six will be the mean area, 

 and being drawn into the altitude of the 

 solid will produce the content : That is, A 

 and a being the areas of the ends, M 

 equal the middle section, then we have 



; 



A + q-f 4M X h 

 6 



solid content. 



is theorem holds good for complete 

 solids as well as frustums, whether right 



There are five species. 



FUC US, in botany, a genus of the Cry p- 

 togamia Algx. Generic character : male 

 vesicles smooth, hollow, with villose hairs 

 within, interwoven : female, vesicles 

 smooth, filled with jelly, sprinkled with 

 immersed grains, prominent at the tip. 

 Seeds solitary. This genus comprehends 

 most of those plants which are commonly 

 called sea-weeds : more than seventy spe- 

 cies are enumerated ; they may all be 

 used to manure land, or burnt for alkali, 

 Some ofthe speciesare eaten, either fresh 

 out ofthe sea. or boiled tender, with but- 

 ter, pepper, &c. If the F. saccharinus ia 

 washed in spring water, and then hung- 

 up in a warm place, a substance like su- 

 gar exudes from it. 



FUEL. Dr. Black divides fuels into 

 five classes ; the first comprehends the 

 fluid inflammable bodies; the second, 

 peat or turf; the third, charcoal of wood; 

 the fourth, pit-coal charred ; and the fifth, 

 wood, or pit-coal, in a crude state, and ca- 

 pable of yielding a copious and bright 

 flame. 



The fluid inflammables are considered 

 as distinct from the solid, on this account, 

 that they are capable of burning upon a 

 wick, and become in this way the most 

 manageable sources of heat ; though, on 

 account of their price, they are never em- 

 ployed for producing it in great quanti- 

 ties ; and are only used when a gentle de- 

 gree, or a small. quantity of heat, is suffi- 

 cient. The species which belong to thisr 

 class are alcohol and different oils. 



The first of these, alcohol, when pure 

 and free of water, is as convenient and 

 manageable a fuel for producing mode- 

 rate or gentle heats as can be desired. 

 Its flame is perfectly clean, and free from 

 any kind of soot ; it can easily be made to 

 burn slower or faster, and to produce less 

 or more heat, by changing the size or 

 number ofthe wicks upon which it burns; 

 for as long as these are fed with spirit, in 

 a proper manner, they continue to yield 

 flame of precisely the same strength. 



