The result of this investigation, expressed in the form of an equation between this energy and the useful work, is called by Moseley the modulus of the machine.

The numerical value of this modulus is o 4342944 81 9 03251 82765 11289..

In the theory of forms we seek functions of the coefficients and variables of the original quantic which, save as to a power of the modulus of transformation, are equal to the like functions of the coefficients and variables of the transformed quantic. We may have such a function which does not involve the variables, viz.

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In portions of the structure liable to important changes of pressure from the rise, and fall of the water and subject to the additional stresses which expansion and contraction by changes of temperature and of moisture induce, and in view of the great difficulty of securing that the average modulus of elasticity in all parts of the structure shall be approximately the same, it is probably desirable to limit the calculated load upon any external work, even of the best kind, to 15 or 20 tons per sq.

The twist or surface-shear being proportional to the torque, the horse-power can be calculated if the modulus of rigidity of the steel employed is known or if the amount of twist corresponding to a given power has previously been ascertained by direct experiment on the shaft before it has been put in place.

Hesse's canonical form shows at once that there cannot be more than two independent invariants; for if there were three we could, by elimination of the modulus of transformation, obtain two functions of the coefficients equal to functions of m, and thus, by elimination of m, obtain a relation between the coefficients, showing them not to be independent, which is contrary to the hypothesis.

It will be observed that in the first process the value of the modulus is in fact calculated from the formula.

The constant -r is called the modulus of decay of the oscillations; if it is large compared with 2irfa the effect of friction on the period is of the second order of small quantities and may in general be ignored.

No Australian timber in the foregoing list has a less modulus than 13,100 lb per sq.

That least distance is called by Moseley the modulus of stability.