384

EXTENSION AND

In all these experiments, both on compression and exten-sion, the deflections and permanent sets were most carefullyobserved and recorded by Mr. Hodgkinson, his principalobject being to deduce formulae for the expression of therelation between the extensions and compressions of bars ofcast-iron, and the weights producing them, in order to supplydata for completing the complicated theory of an abstractbeam composed of a material whose elasticity is imperfect.

The relation between the extension and compression ofbars of cast-iron 10 feet long and 1 inch square, and theweights producing them, is included in the following formulae:

Extension iu = 116117e— 201905e 2Compression w = 107763d— 36318c? 2

w, d, and e, representing the weight, compression, and exten-sion in inches.

For a bar of any other length, l inches, the formulaebecome,

Extension w = 13934040 ^ —2907432000 —

l I s

„ d d 2

Compression w = 12931560 j- 522979200-^-

And in order to determine experimentally the error pro-duced by employing these formulae, the following summary ofexperiments on compression and extension was prepared, theerror in parts of the true weight being given in the lastcolumn.