LECTURES. 201 



The attraction between all bodies at sensible distances proved by 

 the experiment of Cavendish. See Mechanics. 



Tlie attraction of all matter the same, shown by an experiment. 

 Also Newton's experiment to prove the same. 



(51.) At all accessible distances above the surface of the earth, the 

 diminution of the force of attraction is very small. If R represents 

 the radius of tlie earth, x the distance^ F the force at the surface, and 

 D the diminution, then approximately 



D=:-?^ (3.) 



Small as this diminution is it may be detected by the vibrations of 

 a pendulum on a high mountain and at the level of the sea. 



In some investigations, as that of the fall of bodies near the earth, 

 &c., the diminution is neglected, and the force is considered as inva- 

 riable : in these cases, gravitation takes the name o1 gravity. 



(52.) The earth is nearly a sphere, and all bodies fall in straight 

 ines, directed nearly to its centre. 



The convergency, however, in a short distance is very small. In a 

 geographical mile it is but one minute of a degree. 



The direction of gravity is readily shown by the plumb line. 



The loeight of a body is the aggregate action of gravity on each of 

 its atoms, or 



W=N(7. (4.) 



Consequently the weight of bodies is as the quantities of matter, and 

 also as the force of gravity. 



(53.) The absolute weight of a body is estimated in reference to 

 some arbitrary standard, which differs in different countries. In 

 England the grain is the foundation of the system of weights. 



Pound avoirdupois (16 oz.) 7000 grains. 

 Ounce do. 43 Y| " 



Pound Troy (12 oz.) 5760 " 

 Ounce do. 480 " 



In order to perpetuate the standard it is referred to the weight of 

 a given hulk of pure water at a given temperature. Thus the En- 

 glish grain is of such a weight that a cubic inch of distilled water at 

 62° F. in vacuo, is equal to 252.72 of such grains. A cubic foot 

 therefore weighs 62.3862 lbs. avoirdupois. 



In the State of New York, by a provisional act of the legislature, 

 the ounce is the standard ; and this is of such a weight that 1,000 of 

 them are equal to the weight of a cubic foot of distilled water at its 

 maximum density (40° F.) and in vacuo. 



(54.) The ratio of the weight of one body to that of another of equal 

 bulk taken as a standard is called the sj^ecijic gravity. 



Pure water at a given temperature is the standard for solids and 

 liquids ; air under a given pressure and temperature for gases and 

 vapours. 



Simple method shown of determining the specific gravity of bodies — 

 other methods will be given under the head of hydrostatics. 



