416 On the Resistance of Solids. 
side compressed; but a horizontal stratum of particles, at or 
near the middle of the depth, will neither be extended nor com- 
pressed. Hence the line representing this stratum, in the sec- 
tion of the bar, is called the newtral line. 
11, The extension and compression of any part of the section 
is proportional to its distance from the neutral line. 
The quantity of extension and compression, and the position 
of the neutral Jine, may be observed in some soft woods, with a 
considerable degree of accuracy, by drawing two vertical lines, 
very near to each other, against oue of the vertical sides of the 
bar at the place of fracture, before the weight is applied. 
Sometimes the parts that have been extended may be distin- 
guished from those which have been compressed by the fracture, 
aud in fibrous substances, by stopping the descent ‘of the bar be- 
fore the fracture is completed, the position of the neutral line may 
be observed. ‘The last is the best method. 
Du Hamel made some experiments on bars of willow, with the 
view of determining the position of the neutral line, by cutting 
the bars to different depths, with a saw, on the compressed side’ * 
but this method is not susceptible of much accuracy. 
12. From many observations, I have found that when the sec- 
tion is rectangular or anaes the neutral line passes through the 
centre of gravity of the ection, or extremely near it. Or, more 
generally, that when me petenel line divides the section into two 
parts, that are equal and similar, it passes through its centre of 
gravity :—and that in triangular sections the distance of the centre 
of gravity from the vertex is about seven-ienths of the height. 
On the transverse Strength of Beams when the neutral Line di- 
vides the Section into two Parts that are equal and similar. 
13. Prop. To determine the strength of a beam fixed at one 
end to support a weight suspended at the other end. 
Let ABC represent the beam; where C is the point of sup- 
ee 
| | 
| | 
E Rg B - 
| | SAREE: hake WR os AE Riles Jo A 
Pine ee I erie Oe 
aD 0H if 
Ae BC the place of fracture, and D the place of ‘the neutral 
ine. ; 
* Transport du Bois, p. 419. Then, 
