450 THE STRENGTH 



on the strength of materials, that if the beam 

 be of equal thickness throughout its depth, 

 the curve should be an ellipse to enable it to 

 support, with equal strength in every part, an 

 uniform load; and if there be nothing but the 

 rims, or the intermediate part be taken away, 

 it is shewn by Hutton in his Treatise on 

 Bridges, or in my Paper, page 364 of this 

 volume, that the curve of equilibrium, for a 

 weight uniformly laid over it, is a parabola : when 

 therefore the middle part is not wholly taken 

 away, the curve is between the ellipse and 

 parabola, and approaches more nearly to the 

 latter, as the middle part is thinner. Mr. 

 Tredgold states the proper form of the curv^ 

 to be an ellipse. 



39. The instrument used in the experiments 

 was a lever, about 15 feet long, placed hori- 

 zontal, one end of which turned on a pivot in 

 a wall, and the weights were hung near to the 

 other ; the beams being placed between them 

 and the wall. In the first 17 experiments, the 

 beams were placed at 3 feet distance from the 

 pivot in the wall, and in the other experiments, 

 at 2 feet, except otherwise mentioned. 



All the beams, in the 22 experiments imme- 

 diately following each other, were exactly 5| 



