1912^ Fundamental Bases of Dynamics 71 



body which weighs 10000 lbs. at 45° latitude, will weigh, on an 

 equal armed balance, 10000 lbs. anyivhere. Such a balance, or 

 any lever balance, will thus give approximate results, which are 

 usually near enough for commercial or most engineering pur- 

 poses. 



(8) To find the difference in weights as measured on "the 

 standard spring balance" at any two points, let W^ and g^ repre- 

 sent the weight and gravity acceleration at one point, W2 and (/g 

 similar quantities for the other point ; then, 



Wi Wo 



- = - (2) 



9i 92 

 Thus if a quantity of tea weighs W2= 1 lb. at the equator, 

 where g2= 32.09, it will weigh at London where g'i= 32.19 



32.19 



Wi= — (1) = 1.003 lb. 



32.09 



(9) Similarly, if any heavy body suspended from a wire, 

 stretches it an amount e at the equator, it will stretch it 1.003 e 

 at London. 



(10) The steam pressure that will just lift a certain body at 

 London, will be 1.003 times the steam pressure, at the same 

 temperature, that will lift the same body at the equator. Other- 

 wise, by proportion, the same steam pressure will lift a body at 

 the equator weighing 1.003 times as much as at London, if the 

 weighing, in this instance, is done on an equal armed balance 

 or its equivalent at both places. In fact, adopting the notation 

 of (8), if the steam can just lift a body weighing W lbs. on the 

 spring balance at London, by assumption, it exerts the same 

 pressure, 



gri 32.19 



W^= — W2= W2= 1.003 W2 



^2 32.09 



at the equator. 



Here W2 is the spring balance weight of the same body at 

 the equator. Hence a second body weighing 1.003 times the 



