Trin: Coll: - Gives his 'critical' comments of WW's treatise on dynamics. He considers WW's enunciation of the laws of motion 'very far preferable to any other that I have seen'. GA emphasises the importance of attaching the same meaning to the word: 'It… read more
Trin: Coll: - Gives his 'critical' comments of WW's treatise on dynamics. He considers WW's enunciation of the laws of motion 'very far preferable to any other that I have seen'. GA emphasises the importance of attaching the same meaning to the word: 'It matters not whether there is at all such a thing as velocity in the world, provided we mathematicians know what we mean by it, and always attach the same meaning to the word. This latter is essential to logical reasoning: and in a science which is not founded on hypothesis but on experiments it is of the greatest consequence that the same word shall signify the same thing in the reports of the experiments and in the mathematical properties founded on them'. Drawing upon Atwood's machine and the philosophy of Locke, GA gives his definition of velocity: 'It is measured by causing the weights (as far as is in our power) to combine during a unit of time in the same rate of motion or at the time for which we desire to find the velocity, and the space thus described is called the velocity. To me the limit of ds/dt is rather difficult to get, but I find no difficulty in conceiving a body to continue to move with the same degree of motion which it has at any time (This perhaps appears absurd - but Locke says that we can comprehend relations between two things without having a clear idea of either)'. GA gives various mathematical corrections to WW's work: 'when I see Mr Whewell led astray in the use of the differential calculus by obscure principles and a bad notation I cannot help wishing that better were substituted'.
