This boat is as yet only in an experimental state, and the first trials of her that have recently been made upon the Saone have shown the necessity of certain modifications that the inventors are now at work upon.—­La Nature.

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A NEW FORM OF FLEXIBLE BAND DYNAMOMETER.

[Footnote:  Read before Section G of British Association.]

By Professor W.C.  UNWIN.

[Illustration:  Fig. 1.]

In the ordinary strap dynamometer a flexible band, sometimes carrying segments of wood blocks, is hung over a pulley rotated by the motor, the power of which is to be measured.  If the pulley turns with left-handed rotation, the friction would carry the strap toward the left, unless the weight, Q, were greater than P. If the belt does not slip in either direction when the pulley rotates under it, then Q-P exactly measures the friction on the surface of the pulley; and V being the surface velocity of the pulley (Q-P)V, is exactly the work consumed by the dynamometer.  But the work consumed in friction can be expressed in another way.  Putting [theta] for the arc embraced by the belt, and [mu] for the coefficient of friction,

  Q/P = [epsilon]^{[mu]^{[theta]}},

or for a given arc of contact Q = [kappa]P, where [kappa] depends only on the coefficient of friction, increasing as [mu] increases, and vice versa.  Hence, for the belt to remain at rest with two fixed weights, Q and P, it is necessary that the coefficient of friction should be exactly constant.  But this constancy cannot be obtained.  The coefficient of friction varies with the condition of lubrication of the surface of the pulley, which alters during the running and with every change in the velocity and temperature of the rubbing surfaces.  Consequently, in a dynamometer in this simple form more or less violent oscillations of the weights are set up, which cannot be directly controlled without impairing the accuracy of the dynamometer.  Professors Ayrton and Perry have recently used a modification of this dynamometer, in which the part of the cord nearest to P is larger and rougher than the part nearest to Q. The effect of this is that when the coefficients of friction increase, Q rises a little, and diminishes the amount of the rougher cord in contact, and vice versa.  Thus reducing the friction, notwithstanding the increase of the coefficient.  This is very ingenious, and the only objection to it, if it is an objection, is that only a purely empirical adjustment of the friction can be obtained, and that the range of the adjustment cannot be very great.  If in place of one of the weights we use a spring balance, as in Figs. 2 and 3, we get a dynamometer which automatically adjusts itself to changes in the coefficient of friction.

[Illustration:  FIG.2 FIG.3]