This is an example of the famous Marin Mersenne balance, an apparatus to estimate the "forces that animate bodies in movement". This matter is of great importance, not only for the benefit to be gained by knowing about it, but also for the significance which it acquired in the history of scientific thought. During the 17th and 18th centuries the subject was debated with great enthusiasm, and some of the most notable physicists and philosophers contributed to the discussion.

The physicists of this time agreed that bodies in movement were animated by "forces" which they were able to measure, indirectly, by studying the effects that they produced. The fundamental issue at stake is, as can easily be concluded, the concept of energy and not force. The intellectual climate had long been prepared for the emergence of the concept of energy but, since scientific knowledge had not reached sufficient maturity to formulate it, this became something of a battle as there were no words to express what was wanted and the argumentation became entangled in a confused web.

Descartes, attempting to evaluate the "forces that animated bodies in movement" through the effects that they produced, concluded that it was possible to do this by knowing the mass and speed of the body, and that the "force" would be proportional to any one of these measurements. Descartes thus identified the "force" with the "quantity of motion" of the body. Alongside Descartes other famous names were to be found, such as Father Mersenne, Gassendi, Desaguliers, Maclaurin, Jurin, Varignon, etc.

However, Leibniz disagreed with Descartes as to the process of evaluating the "forces that animated bodies in movement". According to Leibniz these "forces" which he called "live forces", should be measured by multiplying the mass by the square of the speed.

The new doctrine caused amazing uproar that continued vehemently for nearly a century. Alongside Leibniz were ranged names as illustrious as those that fought in the Cartesian armies, including Johann Bernoulli, Wolf, 's Gravesande, Bulsinguer and others. The battle extended to the theoretical and experimental fields, and the same apparatus that in the Physics Laboratory demonstrated the correctness of Descartes' theory, also demonstrated, in the hands of the opposition, that the doctrine of Leibniz was the more exact.

In the schools, as in the textbooks, the most cautious expounded the two doctrines, respecting the one and the other, since it was men of such great importance who were in dispute over the matter. This was what Musschenbroek did, with justified caution. However, this was not the case with dalla Bella who, in his Physices Elementa edited in 1789, taught that Leibniz's doctrine was totally wrong. Teodoro de Almeida, five years before the publication of Physices Elementa, had already affirmed, in volume II of Cartas Físico-Mathematicas, to his disciple Eugénio: "I, friend Eugénio, also felt great aversion to agreeing with Leibniz, and to rejecting the way of measuring forces by the quantity of motion; and because of the aversion that I felt, and the reasoning that perplexes me, I can understand why the other are confused and climb up walls in order to make the experiments agree with his doctrine, experiments that all prove the opposite."

The name of Father Marin Mersenne (1588-1648) is well known, an intimate friend of Descartes, whose monastic cell served as the meeting place for the discussion of scientific themes and was the origin of the future Académie des Sciences. Mersenne invented a balance, named after its author, designed to measure the effects of the "forces".

Mersenne balance is composed of a beam having equal arms from which the pans are suspended at quite different levels. The lower one is covered with soft clay approximately one inch in thickness with a very smooth surface, over which a metal sphere will be permitted to fall, a sphere that is initially suspended from the same arm of the beam. The higher pan has another one made of wood under it, joined to the column that supports the balance, the higher pan remaining a little above the wooden one when the beam is horizontal.

The balance is equilibrated by placing weights in the higher pan and having the sphere suspended from a certain height over the other. On cutting the thread that suspends the sphere, it falls into the clay, making a hollow in it, whose depth depends on the height and the weight of the sphere. Then, the maximum weight which should be placed in the higher pan and which is susceptible to bouncing in the pan when the sphere falls on the other, is sought. By repeating the operation with the same sphere, released from various heights, a relationship may be established between the values of these heights and the respective values of the weights that bounce when the sphere falls.

Mersenne concluded that the heights of the falls are in direct relation to the square of the maximum weights that can be made to bounce. 's Gravesande, repeating the experiments, came to another conclusion, affirming that the values obtained are directly proportional between themselves.