In rotatory motions we are to consider, that every atom which is at rest requires a certain power to cause its re moval: and that, when one part of a. wheel moves, the whole must move ; therefore the power must be such as is equal to move the whole. hence we find, that, in a well balanced wheel, the motion is easy, because there are as many atoms disposed to descend as there are to be raised ; consequently, the opposing atoms are held in equilibrio. We must observe, however, that the resistance to motion is greater as we approach the cen tre ; for a power which would give a wheel motion when applied at its peri meter, or exterior, would be inadequate to set it in action if applied near to the axis. Therefore, powers applied at the great est distance from the centre have more force than such as are applied nearer to the centre : their effects will be in exact ratio with the squares of their distances from the centre, while the imparted ve locity will diminish in exact proportion with the accession of force. Of this we see innumerable instances in clocks, cranes, and other machines, in which one wheel is made to move another, or in any system of wheels. We cannot, indeed, have a more familiar demonstration than is afforded by the greater facility with which the hind wheel of a coach revolves, com pared with the fore wheel, which, being so much smaller, has the power (al e. the earth) so much nearer its axis, and con sequently revolves with an increase of velocity proportioned to its difference of diameter.
Before we quit this article it may be proper to observe, that the principles of gyration and of oscillation have a close connection with the foregoing points. The powers of windlasses, winches, or cranes, jacks, &c. all depending upon the appli cation of a power at more or less distance from the centre. Thus we find the com
mon steelyard is affected by the removal of the pea, or shifting resistance, along a scale, whereon the power is indicated to augment, according as it recedes from the point of oscillation. But we see, that, in scales equally removed from that cen tre, the perpendicular distances of the weight, or of the goods to be weigh ed, do not in any degree change the pow er, when the two points of suspension are equidistant from the centre of oscil lation ; and that the two scales, together with their suspending chords, &c. are perfectly counterbalanced. A reference to fig. 10 will exhibit, that, provided the two arms, or suspending points, A A, be equally removed from the point of oscil lation, C, it matters not whether the scales be at.equal distances below A A respec tively, or whether one scale be at D and the other at E, provided all their respec tive parts be perfectly equipoised ; but if one arm should be longer, so as to remove one scale further from the centre of os cillation, by giving unequal distances, C A and C F, between the two parts of suspension, their state of equilibrium would be thereby totally destroyed.
We shall now finally observe, that in every branch of mechanics it will be found that equable motion is the surest, the safest, and the most durable ; and that, in proportion as the forces, and the re sistances thereto, are broken or fluctu- ating, so will the former be diminished and the latter be increased. Hence ex perience shews us, that windmills wear more than water-mills, and that animal powers are apt to tear machinery to pieces. We can command an uniform supply of force where water is the power ; but hitherto no means have been found so completely to regulate either the quantity of wind, or the paces of cattle.