PRACTICAL UTILITY OF MECHANICAL PRINCIPLES. 



ureas of all circles are in exact proportion to 

 the squares of their radii, or half diameters.&quot; 

 If, (or example, we draw a circle with a pair of 

 compasses whose points are stretched 4 inches 

 asunder, and another with an extent of 8 inches, 

 the large circle is exactly four times the size or 

 area of the small one. For the square of 4 

 is = 16, and the square of 8 is = 64, which is 

 four times 16. And as the circumferences of 

 1he circles are in proportion to the radii, it will 

 follow, that the length of a string which would 

 go round the curve of the larger circle is ex 

 actly double the length of one which would go 

 round the lesser. Mechanics, in recognising 

 such theorems, will meet with many opportuni 

 ties of reducing them to practice. Again, there 

 is a figure which Geometricians term a parabola, 

 which is formed every time we pour water for 

 cibly from the mouth of a tea-kettle, or throw a 

 stone forward from the hand. One property of 

 the parabola is, that if a spout of water be di 

 rected at half a perpendicular from the ground, 

 or at an angle of elevation of 45 degrees, it will 

 come to the ground at a greater distance than 

 if any other direction had been given it, a slight 

 allowance being made for the resistance of the 

 air. Hence the man who guides the pipe of a 

 fire-engine may be directed how to throw the 

 water to the greatest distance, and he who aims 

 at a mark, to give the projectile its proper di 

 rection. To surveyors, navigators, land-mea 

 surers, gaugers and engineers a knowledge of 

 the mathematical sciences is so indispensably 

 requisite, that without it, such arts cannot be 

 skilfully exercised. 



C 



pie. In like manner the lines AD, and B D, A Band 

 B E, will stand at right angles to each other; and 

 the same will be the case to whatever point of the 

 circle such lines are drawn. The practical appli 

 cation of this principle, in various operations, will, 

 at once, be obvious to the intelligent mechanic, es 

 pecially when lie intends the two ends or sides of 

 iny piece of machinery to stand perpendicular to 

 each other. 



5 



The physical sciences are also of the gieatest 

 utility in almost every department of art. To 

 masons, architects, ship-builders, carpenters 

 and every other class employed in combining 

 materials, raising weights, quarrying stones, 

 building piers and bridges, splitting rocks, or 

 pumping water from the bowels of the earth, a 

 knowledge of the principles of mechanics and 

 dynamics is of the first importance. By means 

 of these sciences the nature of the lever and 

 other mechanical powers may be learned, and 

 their forces estimated the force produced by 

 any particular combination of these powers cal 

 culated and the best mode of applying such 

 forces to accomplish certain effects, ascertained. 

 By a combination of the mechanical powers the 

 .smallest force may be multiplied to an almost in- 

 definite extent, and with such assistance man hau 

 been enabled to rear works and to perform ope. 

 rations which excite astonishment, and which 

 his own physical strength, assisted by all that 

 the lower animals could furnish, would have 

 been altogether inadequate to accomplish. An 

 acquaintance with the experiments which have 

 been made to determine the strength of materials, 

 and the results which have been deduced from 

 them, is of immense importance to every class 

 of mechanics employed in engineering and 

 architectural operations. From such experi 

 ments, (which have only been lately attended tc 

 on scientific principles) many useful deductions 

 might be made respecting the best form of mor 

 tises, joints, beams, tenons, scarphs, &c. ; the 

 art of mast making, and the manner of disposing 

 and combining the strength of different, sub 

 stances in naval architecture, and in the rear 

 ing of our buildings. For example, from the 

 experiments now alluded to it has been deduced, 

 that the strength of any piece of material depends 

 chiefly on ils depth, or on that dimension which 

 is in the direction of its strain. A bar of timber 

 of one inch in breadth, and two inches in depth 

 is four times as strong as a bar of only cvne inch 

 deep ; and it is twice as strong as a bar two 

 inches broad and one deep, that is, a joint or 

 lever is always strongest when laid on its edge. 

 Hence it follows, that the strougest joist that 

 can be cut out of a round tree is not the one 

 which has the greatest quantity of timber in it, 

 but such that the product of its breadth by the 

 square of its depth shall be the greatest pos 

 sible. Again, from the same experiments it is 

 found, that a hollow tube is stronger than a solid 

 rod containing the same quantity of matter. This 

 property of hollow tubes is also accompan : ed 

 with greater stiffness ; and the superiority in 

 strength and stiffness is so much the greater as 

 the surrounding shell is thinner in proportion to 

 its diame .er. Hence we find that the bor.e.s of 

 men and other animals are formed hollow, which 

 renders them incomparably stron^r aiid stiffer, 

 gives more room for the insertion of muscles. 



