PHYSICAL SCIENCE. 



accustomed to spend whole days in the deepest 

 investigations, and was wont to neglect his food 

 and forget his ordinary meals, till his attention 

 v.-as called to them by the care of his domestics 

 His studies were particularly directed to the 

 measurement of curvilinear spaces; and he in- 

 vented a most ingenious method of performing 

 such measurements, well known by the name ol 

 the Method of Exhaustions. 



When it is required to measure the space 

 bounded by curve lines, the length of a curve, 

 or the solid bounded by curve surfaces, the in- 

 vestigation does not fall within the range oi 

 elementary geometry. Rectilinear figures are 

 compared on the principle of superposition ; bul 

 this principle cannot be applied to curvilinear 

 figures. It occurred to Archimedes, that by in- 

 scribing a rectilinear figure within, and another 

 without the figures, two limits would be obtain- 

 ed, the one greater and the other smaller than 

 the area required. It was evident that, by in- 

 creasing the number, and diminishing the sides 

 of these figures, these two limits were made con- 

 tinually to approach each other. Thus they 

 came nearer and nearer to the curve area which 

 was intermediate between them. He observed, 

 by thus increasing the number of sides for a 

 great number of times successively, that he ap- 

 proached a certain assignable rectilinear area, 

 and could come nearer to it than any difference 

 how small soever. It was evident that this 

 rectilinear area was the real size of the curvilinear 

 area to be measured. It was in this way that he 

 found that two-thirds the rectangle under the 

 abscissa and ordinate of a parabola, is equal to 

 the area contained by the abscissa and ordinate, 

 and that part of the circumference of the para- 

 bola lying between them. In the same way he 

 obtained an approximate measure of the area of 

 Hie circle, demonstrating that if the radius be 

 unity, the circumference is less than 3,}-g, and 

 greater than 3^-?. His two books on the sphere 

 nnd cylinder were conducted by a similar method 

 of reasoning. He measures the surface and 

 solidity of these bodies, and terminates his trea- 

 tise by demonstrating that the sphere (both in 

 surface and solidity) is two-thirds of the circum- 

 scribed cylinder. 



In the same spirit his Treatise on Conoids 

 Mul Spheroids was conducted. These names he 

 gave to solids formed by the revolutions of the 

 conic sections round their axis. We pass over 

 his researches on the spiral of Archimedes, 

 as it is usually called, though in reality discover- 

 ed by Conon, one of his friends ; but must notice 

 the Treatise entitled Psammiles, or Arenaritts. 

 Some persons had affirmed that no number, how- 

 ever great, was sufficient to express the number 



of grains of sand situated on the sea-shore. This 

 induced Archimedes to write his treatise, in 

 which he demonstrates that the fiftieth term of a 

 decuple increasing progression is more than suf. 

 ficient to express all the grains of sand contained 

 in a sphere, having for its diameter the distance 

 between the earth and sun, and totally filled with 

 grains of sand. The treatise is short; but 

 abstruse in consequence of the imperfect method 

 of expressing numbers employed by the Greeks. 

 Were our figures substituted for the Greek 

 letters, the reasoning would be sufficiently 

 simple and clear. 



Archimedes did not confine himself to pure 

 mathematics ; he turned his attention likewise to 

 mechanics, and may, in some measure, be con. 

 sidered as the founder of that important branch 

 of physical science. He first laid down the true 

 principles of statics and hydrostatics. The 

 former he treats in his work entitled Isorropica 

 or De Equiponderantibus. His statics are founded- 

 on the ingenious idea of the centre of gravity, 

 which he first conceived, and which has been so 

 advantageously employed by modern writers on 

 statics. By means of this principle, and a few 

 simple axioms, he demonstrates the reciprocity 

 of the weight, and the distance in the lever and 

 in balances, with unequal arms. He determined 

 the centre of gravity of various figures, particu- 

 larly of the parabola, with great ingenuity. 



His discoveries in hydrostatics were the con- 

 sequence of a query put to him by king Hiero. 

 This monarch had given a certain quantity of 

 gold to a jeweller to fabricate a crown, and he 

 suspected that the artist had purloined a portion 

 of the gold, and substituted silver in its place. 

 Archimedes was requested to point out a method 

 of determining how much gold had been pur- 

 loined, and how much silver substituted. The 

 method, it is said, occurred to him all at once, 

 while in the bath, and he was so transported with 

 joy, that he ran naked through the streets of 

 Syracuse, crying out, w% yxx, fvf>r,xx, I have found 

 it, I have found it. The discovery with which 

 he was deservedly so delighted was this, "Every 

 body plunged into a fluid loses as much of its 

 weight as is equal to the weight of a quantity of 

 the fluid equal in bulk to the body plunged in." 

 This discovery furnished him with the method of 

 determining the specific gravity of pure gold and 

 pure silver. These being known, he had only 

 ;o take the specific gravity of the crown, which 

 'supposing no alteration in volume when the two 

 netals are melted together) would enable him to 

 discover how much gold and how much silver it 

 contained. 



This first principle being known, Archimedes 

 deduced from it various other well-known hydro- 



