Our units of linear extension are the lengths of masses of matter or thespaces between marks made on the masses, and we assume these lengths, orthese spaces between marks, to remain unchanged while the temperature isunchanged. From the standard-measure preserved at Westminster, are derivedthe measures for trigonometrical surveys, for geodesy, the measurement ofterrestrial arcs, and the calculations of astronomical distances, dimensions,etc., and therefore for Astronomy at large. Were these units of length, originaland derived, irregularly variable, there could be no celestial dynamics,nor any of that verification yielded by it of the constancy of the celestialmasses and of their energies. Hence, persistence of the space-occupying speciesof force cannot be proved, for the reason that it is tacitly assumed in everyexperiment or observation by which it is proposed to prove it. The like holdsof the force distinguished as energy. The endeavour to establish this bymeasurement, takes for granted both the persistence of the intrinsic forceby which body manifests itself as existing, and the persistence of the extrinsicforce by which body acts. For it is from these equal units of linear extension,through the medium of the equal-armed lever or scales, that we derive ourequal units of weight, or gravitative force; and only by means of these canwe make those quantitative comparisons by which the truths of exact scienceare reached. Throughout the investigations leading the chemist to the conclusionthat of the carbon which has disappeared during combustion, no portion hasbeen lost, what is his repeatedly-assigned proof? That afforded by the scales.

In what terms is the verdict of the scales given? In grammes -- in unitsof weight -- in units of gravitative force. And what is the total contentof the verdict? That as many units of gravitative force as the carbon exhibitedat first, it exhibits still. The validity of the inference, then, dependsentirely upon the constancy of the units of force. If the force with whichthe portion of metal called a gramme-weight tends towards the Earth, hasvaried, the inference that matter is indestructible is vicious. Everythingturns on the truth of the assumption that the gravitation of the weightsis persistent; and of this no proof is assigned, or can be assigned. In thereasonings of the astronomer there is a like implication, from which we maydraw the like conclusion. No problem in celestial dynamics can be solvedwithout the assumption of some unit of force. This unit need not be, likea pound or a ton, one of which we can take direct cognizance. It is requisiteonly that the mutual attraction which some two of the bodies concerned exerciseat a given distance, shall be taken as one; so that the other attractionswith which the problem deals, may be expressed in terms of this one. Suchunit being assumed, the motions which the respective masses will generatein one another in a given time, are calculated; and compounding these withthe motions they already have, their places at the end of that time are predicted.

The prediction is verified by observation. From this, either of two inferencesmay be drawn. Assuming the masses to be unchanged, their energies may beproved undiminished; or assuming their energies undiminished, the massesmay be proved unchanged. But the validity of one or other inference dependswholly on the truth of the assumption that the unit of force is unchanged.