principles which are vital to its character, it has made no advance for half a century; and, to-day, the most talented engineers can say no more, in truth, for their splendid steamers, than that they are constructed perfect in their kind. If they go from the workmanship to the elementary principles, and follow the developments of the mechanical functions of the steam, they can only trace and sum up the lesser half of those functions in the motion of the sea-going ship, and will vary but little from one-half to the best inland steamers.

We cannot discard the usefulness of our present systems, (the screw being still less mechanical than the wheel,) spendthrifts though they are, until the usefulness of a new system shall supersede them; but a mechanical system will only waste power in retrograde slip; for this, to a certain extent, cannot be avoided, yet this, by the new system, will not exceed, if it shall equal, 20 per cent to steamships. All the other wastes now submitted to are remedied by the inherent mechanical virtue, and 20 per cent from the 55 per cent now wasted, will add 35 per cent of useful power to the 45 per cent now useful, making a moving power of 80 per cent instead of only 45 per cent; also, this supplementary 35 per cent exceeds three-fourths, or 75 per cent, of the 45 per cent.

Whatever the devices and improvements for generating power, or a greater quantity of power, it is highly important that the mechanical functions thereof shall be economically used.

And to the present sources of generating power, we shall soon be without excuse if we do not make passages in the same time now made with a largely reduced rate of consumption of fuel, and quantity; or, secondly, if we do not make passages in less time to the same rate of fuel-the quantity being reduced as the time is reduced; or, thirdly, if we do not make passages in considerably reduced time with an increased rate of fuel(by increase of boilers and machinery to burn the greater quantity in the lesser time,) the quantity being the same as now used.

INCOMPETENCY OF THE CRANK ENGINE TRANSMISSIONS TO UTILIZE OVER FOUR-FIFTHS OF THE POWER OF THE STEAM.

As every line of application of power to the crank is oblique-excepting the line of perpendicular action at the living center-and variably so through every possible obliquity twice per piston stroke, a careful examination of a single angle of obliquity forms the bases of computation of all other angles.

Mechanical value of a given amount, or a given number of cubic inches, of steam expended at the angle of 30° to the crank, compared to its value expended in. perpendicular action. To the oscillating engine, in fig. 1, let aa' equal the motion of the piston, and represent a given number of cubic inches of steam. Then, at this angle of 30°, as Abs or dbs, crank-pin space be equals twice piston space aa', and the tangential pressure at b equals half the applied pressure.

Let space ' equal space aa', then as sm equals twice sl, or radius,

2

space mn equals space bc, and the pressure at m equals half the pressure at l. But the velocity of piston when connected at b, is only half its velocity when disconnected at b and connected at l.

This is shown by observation, (as also by demonstration,) as, since the tendency of the piston to velocity at the dead center (as in Ags) is zero, when the pressure of rotation is zero, and since the tendency of the piston to velocity increases from zero to full velocity at the living center, (as if cylinder A is changed from Ags to Abs, and more to Bbs,) just as the pressure of rotation increases from zero to full; and as the pressure of rotation increases from zero as the sines of the angles of obliquity increase, so the velocity of piston increases as the sines of the angles of obliquity increase, or varies as the sines of the angles vary.

Hence, as the sine of the angle of piston velocity at 30° (as sl in direction Abd) equals half radius, or radius, and in perpendicular action (as sb in direction Bbd') equals radius, the velocity of piston at b in Abd is only half its velocity at b in Bbd'.

2

But the velocity of piston at b in direction Bb is the same as at lin direction Al, the pressures at points d and I being equal; because both are simple perpendicular actions, and the power of the steam in each is instantly transmitted.

(a)

(b)

(c)

Consequently, the velocity of the piston in Ab connected at b, is only half its velocity in Al connected at l.

Further, as the velocity of piston A is only half the velocity of crank-pin b, and is only half the velocity of piston when connected at l, it is true that the velocity of piston connected at l equals the velocity of crank-pin connected at b.

Hence, the mechanical duty exerted by the steam upon point b is 100 lbs. pressure into the velocity of crank-pin.

Also, the mechanical duty exerted by the steam upon point lis (d) 100 lbs. pressure into the velocity of crank-pin, as the velocity of point l equals that of crank-pin b. (See marginal reference b.)

The expenditures of steam are measured by aa' when in oblique action through be, and by aa' equal l' in perpendicular action through W'; therefore, the primary cost and mechanical values of the steam expended are equal, and in each case are represented by 100 lbs. pressure into velocity of crank-pin. (See c and d.)

(e)

But the UTILIZED value in bc is not the 100 lbs. pressure exerted upon the crank-pin b, but the pressure of rotation derived from it, which is only half of 100 lbs., or 50 lbs., and only equals 50 lbs. tangential pressure into velocity of crank-pin, or 50 x v.

And the UTILIZED value in ll' equals 100 lbs. pressure into velocity (f) of crank-pin. Its equivalent in space mn, equal bc, is 50 lbs. into twice the velocity of crank-pin, or 50 × 2v.

That is, if aa', ll' each equal one inch, bc, mn each equal two inches, then the same number of cubic inches of steam, and same intensity of pressure, which, when connected at b can only move 50 lbs. 2 inches in bc, in an instant of time t, when connected at I can move 50 lbs. 2 inches in mn, in one-half of the same instant of time t, or with double velocity.

Therefore, the quantities of steam, the loads moved, and the spaces, all being respectively equal, the UTILIZED VALUE OF THE STEAM is as the velocities, which are as velocity v in bc is to velocity 2v in mn, or asis

to 1.

The difference in the utilized values derived from the steam equals the wasteful expenditure, in consequence of developing it through the antimechanical relations of the obliquity of 30° to the crank.

Again; to harmonize the velocity of piston, when connected at b, with its velocity when connected at 7, we must extend relief to the functional element of pressure exerted at b, which we may do by reducing the resisting load in be from 50 lbs. to 25 lbs., or one-half, and we thereby double the constituent element of velocity.

(9)

We have, then, a utilized value of 25 lbs. 2 inches in be in half of the former time, or in one-half of instant of time t, or with velocity 2v, and in mn of 50 lbs. 2 inches, in half of instant of time t, or velocity 2v.

Therefore, the quantities of steam, the spaces passed, and the times, being respectively equal, the utilized value of the steam in oblique action is to that in perpendicular action as their respective loads, which are as

25 lbs. is to 50 lbs.

(The spaces be, mn may be treated as so extremely small that the difference of angles Abs, Acs would not be appreciated.)

We thus show that the useful effect sought for from a given amount of steam in oblique action, at the angle of 30° to the crank, is only half that due to, and realized from, the same steam in perpendicular action.

And what is true of one oblique force, of x cubic inches of steam, compared to the same force of a cubic inches of steam in mechanical action, is true of all other obliquities, according to their respective angles and relations.

The philosophy of these values is simple, and is that the force-or motive functions of the steam-acts in the direction bd, in which line it cannot move a hair's breadth, being rigidly intercepted in bs-it therefore reacts in direction be, and derives from itself a sufficient quantity of force to change its direction from its line of impossible motion to a line of possible motion, which is the tangential line bf. The quantity of force thus expended equals bd-bf, and can no more be utilized than if the same quantity was expended upon friction. (These relative values are entirely irrespective of friction.) That utilized equals bƒ.

If, for the reactive force in line of crank as in be, we remove the crank and substitute an additional force in same line and direction sb, equal to be, or cosine of the angle-force A being equal to radius-then the joint

resultant of this larger quantity, equal to bd + be, is still diagonal bf of parallelogram bdfe. Now the quantity of force wasted, in order to utilize their mechanical functions in this direction, equals bd + be-bf. That utilized equals bf.

Again; we may examine the same values by the familiar laws of composition and decomposition of forces.

We may resolve the force A, as before considered, into two equal forces PQ, each equal to half A, or radius, and each acting at the same angle

2

of 30° to crank bs. Then the action of P is represented by be in its primary value and direction, and that of Q by be; and their tangential or utilized value by their diagonal bd of parallelogram bede. And bc + be equals radius; and bd equals radius, equals sl or bf in fig. 1, because it is the

2

sum of the sines of the angles PQ, or equals sine of 2 x radius, and sl equals sine of radius.

2

Qacts the same upon the crank as P would if crank-pin 6 had revolved to g; and PQ being in simultaneous action at equal obliquities to rotate crank-pin 6 in tangent direction bd, P must exert a portion of its force to change the direction of Q from be to bd, and Q must exert a portion of its force to change the direction of P from bc to bd, as bd is the only direction in which P or Q can move the least fraction of an inch.

The primary or net mechanical value of P+Q equals bc + be, but their utilized value only equals bd, or half of bebe.

We cannot equivocate from the quantity of power or steam expended, as whatever the quantity and intensity, it is represented by bc + be, the useful resultant of which is oniy half the expended value.

The difference between the primary and the utilized value, is the value wasted by changing the obliquities of action to their tangential directions. Friction has no element in these relations, but is external or correctional to them, because we may centralize the resistance or load at point b, and remove the crank bs, and the respective values are unchanged; hence, the waste of power by this obliquity of action is irrespective of, and in addition to, friction.

We may show the variable relations of utilized values by varying the forces PQ more and more obliquely until they merge in the "dead center," or right line sb, when the diagonal continually lessens from bd until And if we lessen the it merges in point b, and the utilized value is zero. obliquities by varying PQ towards Bb, as at pq, at the angle of 45°, the diagonal equals br of parallelogram btru, or 70 per cent of P+Q; and as we further move them more and more towards Bb, until they are merged in line Bb, the diagonal increases more and more until it equals bf, which equals be + be, or radius.

ILLUSTRATION, True to our obsERVATION, WHICH SHOWS 78 PEr cent of STEAM IN MECHANICAL ACTION EQUIVALENT TO 100 PER CENT IN STEAM UPON THE CRANK.

Let the square of the figure represent a steam cylinder of 100 inches diameter, or 7,854 inches area of piston, and 100 inches stroke, as in AK, and consider the connecting rod to the crank as if infinitely long; and divide the crank-pin stroke into ten equal spaces; and then, as the piston

moves from the "dead center" A to B, the crank-pin has moved through the first tenth of its stroke, and as piston moves from B to C, the crank-pin moves through its second tenth; and so on successively and relatively to the "dead center" K.

From A to B, the capacity of

A

the cylinder equals 19,242 cubic inches of steam; from B to С 55,764 cubic inches, and variably on. The pressure upon the crank-pin to a net of 10 lbs. per inch, equals 78,540 lbs. (or 35 tons) to every indivisible space in AK, and the average utilized pressure at the crank-pin from A to B equals 12,135 lbs.; from B to C 35,225 lbs., and variably on; from which we make this table :

From A to K............

The piston velocity is reduced below the velocity at F, and to zero at A and K, just as the pressures are reduced below 78,540 lbs. at F, and to zero at A and K. Hence, as the piston and crank-pin velocities at Fare identical, the crank-pin velocity is the velocity due to the piston at every