# Decision method for elementary algebra by Seidenberg A.

By Seidenberg A.

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Example text

Will bear to the volume specific For if V, vities, 62 V be the volumes, and s, s' the specific gra- = the weight of the body = the weight of the displaced = 62 5 V's', V: V' = 8':s. 5 Vs fluid . /. To find the conditions of equilibrium of a solid float60. ing in liquid and partly supported by a string. First, let the solid be homogeneous and wholly immersed then the centres of gravity of the solid and of the liquid displaced will be the same, and the direction of the string must be the vertical through the centre of gravity.

It follows therefore that such a rotation will not affect the position of the centre of pressure of any area upon the plane. 50. If a plane area is immersed vertically to a given if the position of its centre of pressure is known, depth, and CENTRE OF PRESSURE. 39 we can determine the position of the centre of pressure for other any given depth. be the position of the centre of pressure, when G, Let the centroid of the area, is at the depth h. If the depth is increased to hf, the increase of pressure on the area acts at G and is equal to K A wA Take the point K' GK - h).

The Pound Avoirdupois contains 7000 grains; one grain therefore very nearly '0648 grammes, or 64*8 milliis, grammes. Again, the metre being 39*370432 inches, or 3-280869 one foot contains 30*4797 centimetres, and one cubic inch contains 16*387 cubic centimetres. Hence it follows feet, WEIGHT. that the litre cubic inches. is 1 very nearly *0353 of a cubic foot, or 9 61 It may be useful to place some of the relations between the English and French measures of length and mass in a tabular form. Length, Area and Volume.