to Transverse Strain in Beams. 401 



h-8, or "6875 inch. It would, however, be impossible to 

 regulate the distance with any very minute accuracy, and 

 some considerable part of the irregularities observable in the 

 measurements may probably be due to this cause. 



" It will be observed," says Mr. Barlow, " that the exten- 

 sions and compressions increase in an arithmetical ratio from 

 the centre to the extreme upper and lower sides of the beam/'' 

 If we substitute the word " neutral axis " for u centre," it is 

 obvious that this must necessarily be the case; and any devia- 

 tion from this law must be regarded as resulting from errors 

 of measurement, inequality in the distances between the 

 points measured, want of uniformity in the material, or other 

 accidental causes. 



It may therefore be assumed that if an arithmetical series 

 be taken, approximating as nearly as possible to all the actual 

 measurements, the quantities so obtained may be regarded as 

 the corrected results of the experiments. 



It is, moreover, to be noted that the extensions and com- 

 pressions measured are those of a portion of the beam about 

 12 inches in length, extending therefore to a distance of about 

 6 inches from the centre on each side. 



Each length was separately and minutely measured before 

 being strained ; but the variations in the original lengths, at 

 least in the first series of experiments, do not exceed -^q th 

 part of the whole, so that they will be inappreciable in their 

 effect upon the amount of extension or compression as 

 measured. The mean length was 12*25 inches. 



But the maximum strain will exist only at the centre of the 



length of the beam, and that at any other part of it must be 



proportionate to its distance from the point of support. It 



follows that the strain at the centre of the beam will be 



42 

 . tt ^ , =1*078 times that indicated bv the measurement of the 

 <5894 



extension or compression in the length of 12*25 inches, or 



nearly one twelfth greater "*. 



The units of measurement in which the extensions and 

 compressions are given by Mr. Barlow are ^gVo'th °f an 

 inch. 



Taking, then, one series of experiments on the same beam 

 subjected to successive loads we find these results : — 



* That is, so long as the limits of elasticity are not exceeded. If the 

 beam should be overstrained at its lower side the strain at the centre 

 may be considerably more in comparison with the mean strain for any 

 distance on each side of the centre. 



