It seems appropriate to insert here the following letter received long after from a very prominent engineer of that day. “LONG BRANCH, N. J., Aug. 7th, 1872. “Mr. CHAS. T. PORTER: “_My dear Sir:_ Since I had the pleasure of reading the paper which you read before the Polytechnic Club last winter, I have regarded your demonstration as not less original than subversive. It is, for the first time I believe, apprehended and asserted, not merely that the _vis inertia_ of the reciprocating masses is not primarily an adverse element in the economy of the crank-engine, but that a certain amount of weight in the piston and its connections, and in high-speed engines a very considerable amount, is an absolute theoretical necessity. “As this will be deemed rank heresy by folks who have been making skeleton pistons of wrought iron, it is well perhaps that you are entrenched at the outset behind the _experimentum crucis_ of loose brasses. “Very truly yours, “JOSEPH NASON.” The following figures represent an elegant invention of Mr. Edwin F. Williams, which exhibits graphically the acceleration and retardation of the reciprocating parts of an engine. In these views, _A_ is the cross-head in its mid-position; _B_ is the lath by which the paper drum of an indicator is actuated through the cord _n_. The lower end of this lath is fixed in its position on the cross-head by the stud _j_, on which it turns freely. _y_ is the end of a vibrating arm, which permits the point of suspension of the lath _B_ to fall below the position shown, as required in the motion of the cross-head on account of the lower end of the lath being so fixed. _d_ is a cylindrical box, partly open, which is secured on the side of the cross-head, in a position parallel with motion, by the arm _P_. The end of this arm is on the stud _j_, inside the lath _B_. It is prevented from turning on this stud by the set-screw _K_, and its fixed position is further assured by the stud _r_. In the box _d_ is the cylindrical weight _h_, running freely on rollers, not shown, and bored to receive a spring _e_, of known strength. This spring is secured in two heads, one of which is screwed into the box and the other into the weight. The force required to move the weight _h_ is thus applied to it through the spring. The operation of this instrument is as follows: The cross-head being at its mid-stroke, as represented, has acquired its full velocity. At this point no force is being exerted, either to impart or to arrest its motion. The same is the case with the free weight _h_. No pressure is here being exerted, either to compress or to elongate the spring _e_. [Illustration: JOSEPH NASON] [Illustration: Fig. 1 Fig. 2 Fig. 5 SCALE 40 265 REVS. PER MIN. 11¹⁄₄″ × 16″ PORTER-ALLEN. Fig. 4 SCALE 40 265 REVS. PER MIN. 4.416 „ „ SEC. Fig. 3