26 REPORT — 1844. 



arises wholly from the weight laid on, and the friction must be almost insensible. 

 The admeasurements of the sets, Mr. Hodgkinson stated, were as accurate as the light 

 of a candle, in addition to bright day-light, would enable the observer, using the ut- 

 most care, to judge. Great care was taken to have the ends of the bars well-supported 

 during the experiments, and when a bar in its natural state was not perfectly uniform, 

 but in some degree twisted, iron wedges filed to the exact form were made and fast- 

 ened to the ends of the bar, that it might rest firmly against the rollers. The length 

 of the bar between the rollers supporting the ends was six feet six inches; and its 

 depth in different materials varied from ■i'oihs of an inch to one inch, or a little more, 

 in the direction in which the bar was bent. The utmost attention was paid to en- 

 sure accuracy, and the time taken up by an experiment was usually from three to five 

 hours, but in some cases a whole day. 



The principal source of error arose, apparently, from the difficulty and almost im- 

 possibility of keeping the long flexible bars operated upon perfectly free from vibra- 

 tion, in the neighbourhood of a large manufactory. Another source of small error 

 might arise from the pressure of the screws at the ends of the straight edge against 

 the ends of the bar, these being held by light springs to keep them always in contact ; 

 but this was avoided by removing them in the experiments on some of the most 

 flexible bars, as those of steel and wrought iron. 



With this apparatus many experiments on bars of different materials have been 

 made, and the deflexion and set from different weights obtained, the leading results 

 from which are below. 



In ribs of soft stone, each sawn seven feet long, four inches broad, and about one 

 inch thick, bent in the direction of their least dimension, the mean deflexion was ob- 

 tained from the same weight laid gently on about four times, for three minutes each 

 time ; and after the bar had been unloaded each time for five minutes, the set was 

 observed. The mean results in different experiments are as follow : — 



Weights laid on. Sets produced. 



lbs. 



[42 

 Experiment !•■{ jj 



U2 



Experiment 2.-^ ^g 



{14 

 28 



Experiment 4.-| oo 

 Experiment 5.1 - 



nch. 



006 



170 



026 



170 



0099 



149 



0369 



1298 



0099 



1271 



0087 



0879 



0280 



0879 



Ll4 



Seeking from above for the power n, of the number expressing the weights to which 

 the sets are proportional, we have (in Experiment 1), 7" : 42" : : "006 : -170; 

 whence we obtain n= 1-866 ; and from the other experiments we have n successively 

 equal to r957, 1-810, 1-840, 1-709, 1-668, 1-650; the mean from the whole giving 

 w=r786. Whence it appears, Mr. Hodgkinson observes, that stone differs in this 

 respect but little from cast iron, the sets varying nearly as the squares of the weights 

 laid on. 



In wrought iron and steel the sets seem to follow a different law, but the exami- 

 nation of these metals has not been completed. In these, as in materials of every 

 description tried, the weights, however small, seemed to produce a permanent set; 

 no body recovering of itself its original form after a change of figure had been produced 

 in it. 



If a small weight was laid, without any acceleration, upon a bar of any material a 

 number of times successively, the set was found to be increased each time. Mr. 

 Hodgkinson read to the Association results of this kind from stone, cast iron, hard 

 and softened steel. He had sought for the longitudinal extension and set in long 



