164 REPORT— 1867. 



wooden frame A, to which were bolted two iron brackets, BE, on which the 

 bars were laid. Immediately over the centre of the bar, at a point equi- 

 distant between the supports, the wheel and screw C was attached to the 

 scale D on which the weights were placed, 56 lbs. at a time ; after each 

 weight was laid on, the deflections were taken, and the experiment was con- 

 tinued until a large permanent set was obtained. The permanent set was 

 observed at intervals in the following manner : — After the deflection pro- 

 duced by the load had been ascertained, the screw C was turned so as to raise 

 the scale and relieve the bar of the load, thus enabling the experimenter to 

 ascertain the eff'ects of the load upon the bar and to register the permanent 

 set. This operation was conducted with great precision, as may be seen on 

 consulting the Tables in the experiments which follow. 



Each of the bars have been treated in this way, care having been taken to 

 secure portions of each bar for the experiments on tension and compression. 

 In addition to these distinct tests, I have the advantage of my friend 

 Mr. Tate's assistance in the reduction of formula; as follows : — 



Formula of Redxjction. 



lor tlie reduction of the Experiments on Transverse Strain, — When a bar 

 is supported at the extremities and loaded in the middle, 



^=4^-^' ^^^ 



where I is the distance between the supports, K the area of the section of 

 the bar, d its depth, iv the weight laid on added to f ths of the weight of the 

 bar, B the corresponding deflection, and E the modulus of elasticity. 

 When the section of a bar is a square, 



E=~ (2) 



These formula} show that the deflection, taken within the elastic limit, 

 for unity of pressure is a constant, that is, — =D, a constant. 



Let -^ _2 J . . . J _!L be a series of values of D, determined by experiment 



in a given bar, then 



J)=l(k + k+...+k\ (3) 



which gives the mean value of this constant for a given bar. 

 Now, for the same material and length, 



^ , or D x Ji^ ; (4) 



lu Kd- ' 



and when the section of the bar is square, 



-,orD(^l (5) 



w a 



If Dj be put for the value of D when J=l, then 



=l('A4.1a+...+!!LVz', (6) 



which expresses the mean value of the deflection for unity of pressure and 

 section. This mean value, therefore, may be taken as the measure of the 



