228 
MR. W. H. BARLOW ON THE RESISTANCE OF FLEXURE 
Determination of the Neutral Axis. 
Measurements of the Second Beam. 
Beam erect. 
Beam inverted. 
No. 1. 
Difference. 
No. 2. 
Difference. 
No. 3. 
Difference. 
No. 4. 
Differenee. 
No. 5. 
Difference. 
No. 6. 
Difference. 
No. 7. 
At rest 
previous to 
being 
strained. 
Strain of 
8000 lbs. 
oil centre. 
Strain of 
16,000 lbs. 
on eentre. 
Strain of 
8000 lbs. 
on centre. 
Strain of 
16,000 lbs. 
on centre. 
Weight 
removed. 
Weight 
removed. 
Mieroineter 
Micrometer 
Micrometer 
Micrometer 
Micrometer 
Micrometer 
Micrometer 
readings. 
readings. 
readings. 
readings. 
readings. 
readings. 
readings. 
1633 
+ 37 
1670 
+ 65 
1735 
-89 
1646 
— 44 
1602 
-56 
1546 
+ 97 
1633 
1525 
+ 28 
1553 
+ 47 
1600 
-63 
1537 
— 24 
1513 
-46 
1467 
-^67 
1534 
1481 
+ 21 
1502 
+ 34 
1536 
-44 
1492 
-19 
1473 
— 28 
1445 
+ 42 
1487 
1442 
+ 11 
1453 
+ 21 
1474 
-23 
1451 
— 10 
1441 
-12 
1429 
+ 22 
1451 
1392 
+ 2 
1394 
+ 7 
1401 
— 1 
1400 
+ 1 
1401 
1401 
+ 4 
1405 
1375 
-10 
1365 
- 9 
1356 
+ 18 
1374 
+ 17 
1391 
+ 11 
1402 
-17 
1385 
1338 
— 18 
1320 
— 24 
1296 
+ 44 
1340 
+ 20 
1360 
+ 27. 
1387 
-35 
1352 
1257 
-27 
1230 
-37 
1193 
+ 64 
1257 
+ 31 
1288 
+ 43 
1331 
-57 
1274 
1248 
— 42 
1206 
-46 
1160 
+ 85 
1245 
+ 44 
1289 
+ 57 
1346 
-78 
1268 
Note . — The extensions are marked + ; the compressions are marked — . 
Considering’ the very minute quantities which had to be measured, and the nume- 
rous causes of disturbance to which observations of so much delicacy were liable, 
such as changes of temperature or want of perfect uniformity in the dimensions or 
texture of the beams, the results, as shown by the column of differences, exhibit 
more regularity than could have been expected ; and they point out the position of 
the neutral axis, as the centre of the beam, in a manner so decided, as to remove all 
further doubt upon this subject, not only in the smaller strains, but in the larger ones 
also ; which, in the case of the second beam, were carried to about three-fourths of 
the breaking weight. 
It will be observed also that the extensions and compressions increase in an 
arithmetical ratio from the centre to the extreme upper and lower sides of the beam. 
These experiments having established the fact that the neutral axis is in the centre 
of a rectangular beam, and that its position is not sensibly altered by variations in 
the amount of strain applied, it becomes evident that if there were no other elements 
of strength than the resistances to direct extension and compression, the well-known 
formula 2adf 
should give the breaking weight when /is equal to the smaller of these two resist- 
anees, which in cast iron is the tensile resistance. But the weight so calculated is 
less than half the actual strength of the beam. 
In considering this question, I was forcibly struck by the circumstance, that, in 
applying the law of “ tensio sic vis" to contiguous fibres, under different degrees of 
tension and compression, the effect of lateral adhesion is omitted, and each fibre is 
