4. Redefining standards
A. Redefining the standard of force using both Newton's second law and the proportionality of weight and inertial mass
At this point another group of scientists comes along and suggests that perhaps Newton's second law is more accurately true than previously established , to someas yet unknow accuracy. They then try to invert the logic and use: 1. the accuracy of F=ma (assumed accurate to a part in 1044) , (2) the accuracy of scale balance measurements of masses (assumed accurate to a part in 1044) , and (3) the accuracy of ruler and clock measurements of accelerations (accurate to a part in 1044). In this way they obtain a new standard, accurate to a part in 1044 for force F (by direct measurement accurate only to a part in 1033). Neverthe less , this does not define F, which continues to come from a true force-measuring device.
because acceleration was setermines in the context of the second law to a part in 1044, acceleration is necessarily accurate for the first law to a part in 1044. However, the third law is independent of the others and must be tested to a part in 1044. If the third law is found to be true to at least that accuracy --- which we assume to be the case-- then the assumptions that the second law is accurate to a part in1044 , and that the proportionality of weight to mass is accurate to a part in 1044, are both consistent. this consistency would thus establish the third law to a much higher degree of accuracy (a part in 1044) than originally established (to a part in 1033 ) --- a significant advancement.