RESISTANCE. 



into that of M. Manotte, but to imagine that the refiitance, 

 or the abfolute weight, is become lefs, every thing elfe re- 

 maining the fame. 



One of the moft curious, and perhaps the mod ufeful 

 queitions in this refearch, is to find what figure a body mult 

 have, that its refiitance may be equal in all its parts, whe- 

 ther it be loaded with an additional weight, or as only fuf- 

 -taining its own weight. 



To this end it is necefl'ary that fome part of it fhould be 

 conceived to be cut off by a plane parallel to the fraAure, 

 fo that the momentum of the part retrenched, be to its re- 

 fiftance in the fame ratio as the momentum of the whole is 

 to its refiftance. Thefe four powers aft by arms of levers 

 peculiar to themfelves, and are proportional in the whole, 

 and in each part, of a folid of equal refiilance. From this 

 proportion Varignon deduces two folids, which fhall refill 

 equally in all their parts, or be no more liable to break in 

 one part than in another. Galileo had previoufly found one 

 of thefe, which is that in which the fides are parabolical : 

 the other, found by Varignon, is in the form of a trumpet, 

 which is to be fixed into the wall by its greater end ; fo 

 that its magnitude or weight is always diminifhed in pro- 

 portion as its length, or the arm of the lever by which it 

 ads, is increafed. It is remarkable, that, however different 

 the two fyftems may be, the folids of equal refiitance are 

 the fame in both. 



We cannot purfue the theory of refiftances to a greater 

 length in the prefent article ; but fhall confine ourfelves to 

 exhibiting a general fynopfis of the moft important refults 

 which have been drawn by different writers on this fubject, 

 both practical and theoretical. 



i. The refiftance of a beam, or bar, to a fracture, by a 

 force acting laterally, is as the folid made by a fection of 

 the beam in the place where the force is applied, into the 

 diftance of its centre of gravity from the point or line where 

 the breach will end. 



2. In fquare beams, the lateral ftrengths are as the cubes 

 of their breadths or depths. 



3. In cylindric beams, the refiftances or ftrengths are as 

 the cubes of the diameters. 



4. In rectangular beams, the lateral ftrengths are conjointly 

 as the breadths and fquares of the depths. 



5. The lateral refiftances of any beams, whofe feftions are 

 fimilar figures and alike placed, are as the cubes of the like 

 dimenfions of thofe figures. 



6. The lateral ftrength of a beam, with its narrower face 

 upwards, is to its ftrength with the broader face upwards, 

 as the breadth of the broader face to the breadth of the 

 narrower. 



7. The lateral ftrengths of prifmatic beams of the fame 

 materials, are as the areas of the fedtions, and the diftance 

 of their centre of gravity, directly, and as their lengths 

 and weights reciprocally. • 



8. When the beam is fixed at both ends, the fame property 

 has place, except that, in this cafe, we muft confider the 

 beam as only half the length of the former. 



9. Cylinders and fquare prifms have their lateral ftrengths 

 proportional to the cubes of their diameters, or depths, di- 

 rectly, and their lengths and weights inverfely. 



10. Similar prifms and cylinders have their ftrength in- 

 verfely proportional to their linear dimenfions. 



For other propofitions relative to the refiftance or ftrength 

 of beams of various forms and in various pofitions, fee the 

 article Strength and Stre/s of Materials. 



The following refults are wholly drawn from experi- 

 ments on different fubftances, by Emerfon and other 

 writers, by means of which the propofitions ltated in 



7 



H 



the preceding part of this article may be fubmitted to 

 computation. 



The relative Refiftances or Strengths of Wood and other 

 Bodies. 



Proportional 

 Refinance. 



Box, yew, plum-tree, oak - - 11 



Elm, afh - - - - 8£ 



Walnut, thorn yl 



Red fir, hollin, elder, plane crab-tree, apple-tree 7 



Beech, cherry-tree, hazel - - 6j * 



Alder, alp, birch, white fir, willow - 6 



Iron - - - - - 107 



Brafs ..... ^o 



Bone - - - - * 22 

 Lead ..... 

 Fine free-ftone ... 



A cylindric rod of good clean fir, of an inch circum- 

 ference, drawn in length, will bear at its extremity 400 lbs. ; 

 and a f pear of fir, of two inches diameter, will bear about (even 

 ton weight. A rod of good iron, of an inch circumference, 

 will bear nearly three ton weight. A good hempen rope, of 

 an inch circumference, will bear icoo lbs. at its extremity. 

 Hence Emerfon concludes, that if a rod of ,fir, or a rope, 

 or a rod of iron, of d inches diameter, were to lift a quarter 

 of the extreme weight that they would fupport, then 



The fir would bear 8i d' hundred weight. 

 The rope - 22 d~ ditto. 

 The iron - 6f d tons. 



To thefe refults we may add, from the experiments and 

 inveftigations of profeffor Robifon, that a prifm of white 

 marble, an inch fquare and a foot long, bears about 500 lbs. 

 And that, from the various authors he has collected, the co- 

 hefive force of a fquare inch of gold, when calt, is about 

 20,000 lbs. ; of filver, 40,000 lbs. ; calt iron from 40,000 to 

 6o,ooolbs. ; wrought iron from 60,000 to 90,000 lbs. ; foft 

 fteel, 12,000 lbs. ; razor fteel, 15,000 lbs. ; oak and beech, 

 in the direction of their fibres, from 8000 to 1 7,000 lbs. ; 

 willow, I2,ooolbs. ; cedar, 5000 lbs. ; fir, 8000 lbs. ; ivory, 

 16,000 lbs. ; bone, 50c o lbs. ; rope, 20,000 lbs. And a 

 cylinder, an inch in diameter, loaded to one-fourth, will 

 carry, if of iron, 135 cwt. ; of rope, 22 cwt. ; oak, 14CWL ; 

 and fir, 9 cwt. 



The refiftance of fome metals is doubled, or tripled, by 

 the operation of forging and wire-drawing ; and the co- 

 hefive, as well as the repulfive, force of wood, is often in- 

 creafed by moderate compreffion. Oak will fufpend much 

 more than fir ; but fir will fupport twice as much as oak ; 

 which difference is fuppofed to arife from the curvature of 

 the fibres of oak ; yet oak has been known to fupport, with 

 fafety, more than two tons for every fquare inch. Stone 

 will fupport from 250 to 850 thoufand pounds, on a foot 

 fquare ; brick, 300 lbs. ; and fometimes they are practically 

 made to fupport one-fixth as much. Stone is laid to be ca- 

 pable of bearing a much greater weight in that pofition in 

 which it is found in the quarry, than in any other pofition. 

 See Strength of Materials. 



Resistance of Fluids, in Hydroflatics, is the force with 

 which bodies, moving in fluid mediums, are impeded and 

 retarded in their motion. 



A body moving in a fluid is refilled from two caufes : 

 the firft, the cohefion of the parts of the fluid. For a 

 body, in its motion, feparating the parts of a liquid, mult 

 overcome the force with which thofe parts cohere. 



The fecond is the inertia, or inactivity of matter, by 



which 



