244 On the Principles of Arckei. 



those of using a greater quantity of materials, and rendering it 

 more difficult to secure the foundations. 



The following method may be used for determining the stabi- 

 lity of an arch experimentally; and also to illustrate the prin- 

 ciples of arches. Let a piece of wood be cut to the shape of 

 the ring of arch-stones, if it be a semi-circle, let it be divided 

 into four equal parts, and make holes through them to meet 

 each other at the joints, connect them to each other, and to the 

 bar AB, with an extensible thread pasvsing through the holes ; 



invert the arch, and let weights, proportional to the pressure of 

 materials on each part, be suspended from its centre of gravity*, 

 then the additional weight required at any part to cause the 

 joints to open will be proportional to the stability. The whole 

 might be cut into the shape of arch-stones, anil weights hung 

 to each piece ; but this causes the experiment to become too 

 complicated. 



It is not necessary that the arcli should be inverted ; for if it 

 was prevented from giving way at the ends A and B, it might 

 be placed over an opening, and the weights suspended by lines 

 from the centres of gravity as before. This last method' might 

 l)e employed with advantage to explain the principles of arches 

 to young students. 



Wo, must not omit to observe, that the centre of gravity of 

 the superincumbent load will not be in the same vertical line 

 with that of the segment of the arch ; but the weights ought to 

 be suspended to a point that would be the common centre of 

 gravity of both the arch and the load above it. 

 I am, sir, 



Your most obedient servant, 

 London, Sept. 25, If 15. T, f, 



* Tlie centre of gravity of the pieces may easily be found by t\\e me- 

 chanical methods described in Gregory's IHeclianics, vol, j. p. 50. 



XLIV. On 



