July 14, 1911] 



SCIENCE 



59 



essential features of the balance. A brass 

 support rests upon a wooden base and carries 

 the knife-edge of a beam made of one eighth 

 inch brass about twenty inches long. The 

 short arm of the beam bears a knife-edge 

 from which is suspended two pans about one 

 and a half or two inches in diameter. When 

 in use the lower pan is in water and the upper 



-^^1-- 



poise is always placed at the same point (in 

 the notch near the end of the beam) x becomes 

 constant. Then the position of the counter- 

 poise when weighings are made in water may 

 be marked on the beam for different values 

 of 0. The equation given above may also be 

 written 



X — 2/ = ^/G- 



one in air. The end of the long arm of the 

 beam rests within a guard supported by an 

 upright which limits the motion of the beam. 

 The long arm is graduated and carries a knife- 

 edge counterpoise with hook at the lower end 

 on which may be hung wire loops. In the 

 figure the counterpoise and the wire loops are 

 about one third actual size. The three knife 

 edges are all in one line. Just above the 

 fulcrum is a device for accurate adjustment. 

 The Graduation of the Balance. — -The long 

 arm of the beam is graduated so that the 

 specific gravity may be read oS directly. The 

 formula for specific gravity by hydrostatic 

 weighing is 



G = A/(A — W); 



where G is the specific gravity, A the weight 

 in air and W the weight in water. Now if 

 we use the same counterpoise with weight p, 

 say, for both weighings, A^px and W = py^ 

 where x and y are distances of the counter- 

 poise from the fulcrum when weighed in air 

 and in water, respectively. The equation then 

 is 



G^px/(px — py), 



from which p may be eliminated, leaving 

 G = x/{x — y). 



Hence the actual weights need not be known. 

 When the weighings are in air, if the counter- 



The distance of the counterpoise from the 

 notch in the beam or x — y is equal to the 

 length of the beam divided by the specific 

 gravity. Thus if x, length of the notch from 

 the fulcrum, is 15 inches (as in the present 

 balance), when G is 2, x — y = 1.5 (15/2). 

 So a point 7.5 inches from the notch is marked 

 2. When Gis3,x — y = 5 (15/3) . A point 

 5 inches from the notch is marked 3 and so 

 on. The graduation is in units from 2 to 10, 

 in tenths from 2 to 4, in fifths from 4 to 6, 

 and in halves from 6 to 10. 



Adjustment. — The short arm, including the 

 pans, is a little heavier than the long arm. 

 But when the lower pan is immersed in water 

 the beam should about balance, as a substance 

 loses weight when immersed in water. Per- 

 fect adjustment is made by the device placed 

 above the fulcrum. But this can be dispensed 

 with, for the position of the beam depends 

 upon the depth of water in the vessel. When 

 no water is in the vessel _ the short arm is 

 heavier than the long arm. So water is 

 poured into the vessel until the beam is bal- 



Use of the Balance. — When in adjustment 

 the balance will look like the figure, the lower 

 pan being in water and the long arm of the 

 beam free. (1) Place mineral in the upper 

 pan. Place counterpoise at the notch near 

 the end of the long arm and counterbalance 



