THE AKCH. 



91) 



arch, notwitlistanding that the weight, form, and size of 

 each bead may vary to any extent. Now we know this 

 only from experience and the belief that natural laws are 

 constant. But on the other hand, if we do know the rela- 

 tive forms, sizes, and weights of every bead, we might find 

 it beyond our powers of calculation to define haforeJiand the 

 precise form of the inverted arch that these beads would at 

 once assume when suspended, unless indeed the problem 

 were simplified by making all the beads equal or varying 

 only in certain symmetrical ratios. Yet, in all cases, if wo 

 wore a.ble to preserve the exact relative positions and bear- 

 ings of these beads forming the inverted arch, when we 

 turned it up they would always form a truly equilibrated 

 arch which would, support itself porfcctly on its two ex- 

 tremities. The powers of Nature so far excel the powers of 

 art. 



Returning again to oiir simple diagram (No. 1), we are 

 supposed to liave here an arch of three stones in perfect 

 equilibrium; this moans that the counterbalancing forces 

 a})plied to the angles B and C in opposite directions should 

 exactly balance one anotlier — consequently, if tJie opposing 

 forces are known, this may be proved by means of the well- 

 known mechanical law of the "parallelogram offerees." 



But in order to apply this law to our diagram with 

 greater olearjicss, let us siippose that the three stones are 

 represented by three stiff rods, AB, B C, and CD, abutting 

 against the fixed points A and D, and let us further suppose 

 that those tliree rods are of tlio same weight as the stones 

 which, they each represent, and that they are in their truly 

 balanced position, though perfectly free to move in the 

 vertical plane. 



It is evident, in the first place, that these balanced rods 

 are only kept in position by the naturally opposing thrusts 



