918

THEORY AND PRACTICE OF ENGINEERING.

Rook II,

Measure of Labour when the Resistance offered is constant. — Supposing the resistance to beuniform, as well as the effort, which is directly opposed to it, and that at the same instantof time it remains the same, it is evident that the work or labour is proportionate to thelength of >vay made; if on a road it will become double or triple, in proportion as thecarriage passes over it: so that if we take labour as unity, or that which vanquishesresistance along a yard of road, the total labour will be the number of yards passed over.Rut should the labour increase at each yard, so that the second should be double, and con-tinue in this proportion, then the labour will be increased in a corresponding manner. As,for example, 1 pound for the first yard, 2, 3, 4 for the second; the labour for each yardwould then be 2, 3, or 4 pounds: taking for unity that force which overcomes theresistance of 1 pound along 1 yard, any labour may be measured by the number of pounds,which express the various resistances of each yard run over. Suppose a moving poweremployed to draw a body along a horizontal plane, the labour must be sufficient to over-come the constant friction which exerts itself, and if this friction be equal fo 40 pounds,and the distance passed over 100 yards, then the labour will be measured by multiplying40 by 100 or 4000 pounds. The rate at which a body moves, or the length of time whichit takes to move from one point to another, is called the velocity ; and this is alwaysproportionate to the force which puts it in motion. The absolute velocity is measured bythe space over which the body moves in any particular period of time, as 10 miles in anhour ; the distance divided by the time gives the velocity per hour. Space is also equal tovelocity multiplied by the time; if the velocity be 10 miles an hour, and the time 10 hours,then 100 miles will have been passed over.

The Value of the mean Effort. — When we have found the value of the mechanical labourof a variable resistance for any length of way run over by its point of action, and dividethat value by the distance, we obtain the mean effort of resistance; or the constant effort,which, being repeated along the road, will produce the same quantity of labour: we havealready shown that for a constant resistance the labour is measured by the product of thatresistance, and the total road passed over.

Various Examples of mechanical Labour. —When a mover is employed in pressing aspring, at each instant it developes an effort which increases as its point of action has goneover a greater distance in the proper direction : this effort may be measured for each posi-tion of the spring, or for each position of the point of action : we may then designate it asa curve, which gives law’s to these efforts, and by approximation calculate the sum of themechanical labour employed at each instant of time, which, united, compose the totallabour. For example, the labour of drawing a body along a plane offering a constantresistance, and which is indicated by compressing a spring, the resistance of which variesat each instant of time. This may be applied to a horse working in a mill, a mandrawing water from a well, sawing or planing timber, polishing metal, &c. The workdone may always be measured by the efforts, equal and opposite, or those contrary to theresistance of the tool employed, the length of that resistance, if it be constant,or by the sum of the products which measure the partial labour, if the resistance bevariable.

In seeking to appreciate mechanical labour, care must be taken not to confound thatwhich the mover effectually expends, and that which immediately results from the workperformed ; for it is easy to imagine that a portion of the first effect is destroyed byother resistances than those arising from the work : it is only to this latter resistance thatthe measure of labour can be applied. To show this, we will instance the whitesmith, inthe operation of filing a bar of metal, on which he must first lean sufficiently to make hisfile bite; he must constantly support the weight of the file, he must exercise another effortto make the file slide over the bar, and this, with a certain rapidity backwards and forwardsto overcome the inertia of the matter contained in it, so that the quantity of work done isthe result of all these varied circumstances. This apparent complication disappears whenwe separate from the result all that is not indispensible to it, bearing in mind what actuallytakes place, where the grains of metal are taken away by the file. ^ e then only see aresistance which supposes an effort equal and contrary to the direction of the way winchthe point of action of the file describes, and the quantity of labour which is measured, as wehave before described. The labour of the mover may be reduced to that only, by sup-posing the file placed fiat on a level bar loaded with a certain weight, and that the moveris employed in regularly drawing this file in the direction of its length, taking into accountthe inertia in the first instance.

'The most simple labour is that of raising a perpendicular weight, provided the inertia benot taken into consideration. The unit of labouring force is sometimes considered to be thatwhich raises a pound one foot in height : a cube metre of water, which weighs 1000kilogrammes, raised one metre in height, is the unit in France ; and this is denominated akilogrammetre. Bolton and Watt’s dynamical unit was one-horse power, equal to raising33,000 pounds one foot in height in a minute, which the French estimate at 7 5 kilogram-metres per second.