giving whence -2=2x, x+y=0, 2x+z=0, Hence the angular acceleration varies as G MR2 In the following example the information obtained is less complete. 5. The range of a projectile on a horizontal plane through the point of projection depends on the initial velocity V, the intensity of gravity g, and the angle of elevation a. The dimensions of range are L. inferences as to the manner in which a enters the expression for the range. The dimensions of this expression will depend upon V and g alone. Assume that the range varies as Vmg". Then 34 CHAPTER IV. HYDROSTATICS. 34. IN the C.G.S. system, density is expressed in grammes per cubic centim. Defining the specific gravity of a substance as the ratio of its density in its actual condition to the density of pure water at 4° C., specific gravity is so nearly identical with density in the C.G.S. system that it is uncertain which is the greater. According to the observations of Kupffer, reduced by Prof. W. H. Miller, the density of pure water at 4° C. is 1-000013. According to the observations of Tralles, reduced by Broch, it is 99988. A fresh determination is in progress at the Bureau International des Poids et Mesures. As regards the density of pure water at 62° F. (16°% C.) in British measures, there is still wider divergence of authorities. Rankine, at p. 99 of Rules and Tables, says 277-123 cubic inches "is the correct volume of 10 lbs. of pure water at 62° Fahr., and is therefore the true value of a gallon in cubic inches. By a former Act of Parliament, since repealed, a gallon was declared to be 277-274 cubic inches." To find the density in grains per cubic inch, we must divide these numbers into 70,000. We thus obtain 252.595 from the value adopted by Rankine, and 252.458 from the erroneous value in the repealed Act. Mr. H. J. Chaney, Warden of the Standards, in the Proceedings of the Royal Society for 1890, No. 294, p. 230, says the hitherto accepted value is 252-458, and gives a new determination from his own measurements, which is 252.286. This value of Mr. Chaney's is equivalent to 997643 gm. per cub. centim.; and as Mr. Chaney adopts 998881 for the ratio of the volumes at 4° C. and 62° F., the density at 4° C. resulting from this determination is 998752 gm. per cub. centim., which differs from the theoretical value unity by 00125-a departure ten times as great as that found by Tralles and Broch, or 100 times as great as that found in the opposite direction by Kupffer and Miller. 35. The table on next page gives the volume of pure water at temperatures from 0° to 100° C. in terms of the volume at 0° C. To compare with the volume at 4° C. it is necessary to add 00017. The values from 0° to 30° are taken from Broch's table, and those from 35° to 100° from a comparison of Rossetti's and Volkmann's. Herr's formula for the volume at t° C., t being between O and 30, in terms of the volume at 0° C. is 1000 0603 t + ·000 007 93 12 000 000 0426 t3. The ratio of the density at 4° C. to the density at 62° F. (16°% C.) is 1·001118 according to the above table, and this is also the value adopted by Rankine (Rules and More exactly, the density of mercury at 0° C., as compared with water at the temperature of maximum density, under atmospheric pressure, is 13:5956. 37. If a body weighs m grammes in vacuo and m' grammes in water of density unity, the volume of the body is m-m' cubic centims. ; for the mass of the water displayed is m - m' grammes, and each gramme of this water occupies a cubic centimetre. Examples. 1. A glass cylinder, I centims. long, weighs m grammes in vacuo and m' grammes in water of unit density. Find its radius. Solution. Its section is r2, and is also m ·m' ; hence 2. Find the capacity at 0° C. of a bulb which holds m grammes of mercury at that temperature. Solution. The specific gravity of mercury at 0° being 13-596 as compared with water at the temperature of maximum density, it follows that the mass of 1 cubic centim. of mercury is 13.596. Hence the required |