202 N. ANNANDALE : 



The equation AL, = WD is equivalent to saying that the weight of the article is 

 equal to the weight of the weight multiplied by the distance of the weight from the 

 fulcrum and divided by the distance of the article from the fulcrum. For convenience 

 of reference these factors may be written weight size, weight position, and article 

 position , thus : — 



A-WD/L or Article size - Weight size x gggggg - 



Accordingly with lever- weighing mechanism, the weight of an article can be 

 determined by observing the amount of variation in the factors on the right-hand side 

 of the equation when they are changed to produce equilibrium. The change may be 

 confined to any one factor alone, the other two being kept constant, this being the 

 simplest method. Or any combination of two factors may be varied, the third being 

 unaltered. Or all three may be varied and noted. This gives seven possible methods, 

 for if there is no variation at all, only one weight of article could be measured, and of 

 course any variety of machine can be used for this purpose by keeping everything 

 constant. 



It is needless to say that there are many other methods of weighing, the spring 

 balance being perhaps the most familiar ; but when levers are employed, all appliances 

 must fall in one of these eight classes whether simple or compound levers are used. 

 It is not proposed here to deal with compound lever machines or machines in which 

 some form of parallel motion or other linkages are introduced in order to enable the 

 weight or load to be placed above the beam without producing unstable equilibrium. 



The possible variations then are : — 



Class. Variable. 



i. Weight size alone, Fig. 3. 

 Weight position alone, Fig. 4. 



Article position alone, Fig. 5. 



Weight size and weight position, Fig. 6. 



Weight size and article position, Fig. 7. 



Weight position and article position, Figs. 8 & 9. 



Weight size and position and article position, Fig. 10. 



No variable. 



These are shown diagrammatically in figs. 3 to 10 in which the article A, the 

 fulcrum F, and the weight W are marked. Class 1 is represented by the ordinary 

 scales or balance ; Classes 2 and 4 by the more ordinary steelyards ; Classes 3 and 5 

 by the less ordinary steelyards ; Class 6 by the bismer or steelyard with a moveable 

 fulcrum fig. 8, or by bent lever apparatus fig. 9, in which the fulcrum is practically 

 fixed while the effective length ratio of the arms alters as the device swings ; Class 7 

 with all factors variable is too complicated for practical use in a simple form ; and 

 Class 8, as said above, only gives one fixed weight. No other type is possible for lever- 

 weighing machines, but the possible variations of structural details are enormous. 



The ordinary scales or balance with equal arms, and a series of weights, is made 

 and used in a thousand different ways. In the crudest shape, a simple stick suspended 



