Hey, >I doubt it. My approach was totally different to >Ing.Saviour's and in my case the system, SI or CGS, >or Imperial for that matter, is totally irrelevant.
But it does matter, in how you divide and compose the derived units. As you say, this stuff can be cut up in any number of ways. Some more meaningful than others. I generally adhere to the notion that !more! dimensions are more enlightening than less, yet the '91 version of me ( allusion to your earlier post ) seemed enamored enough of the LT system to write several pages of notes... >In fact my derivation led to mass being T/L whereas >his gave T^3/L^3 - but that difference is merely >cosmetic. >I took a longer, less mentally traumatic route to >show that mass had the dimensions of [T].[L]^-1 I look forward to seeing it. I seem to remember somewhere else running into the notion of momentum being more fundamental than mass. >Ing.Saviour has part of the maths on his website. >When I've OCR'd it I'll put the whole Note on my >web site for you to read. I seem not to have the link anymore... What is it? Here's my derivation based on the CGS style of a fundamental definition using the force law. As you may know, the basic quantities of magnetic and electric charge are derived units based on the inverse square force laws ( Coulombs law ). ----------------------------------------------------------- LT System : Units for the derived quantity of mass ----------------------------------------------------------- Newton's law has the gravitational attraction between two masses as (1) F = GM^2L^-2 with G being a constant having dimensions (2) G = M^-1L^3T^-2 so that relation (1) can be satisfied. The old CGS system used Coulombs laws to define the basic quantities of magnetic and electric charge. This stands distinct from the SI system which uses a velocity ( C ) to tie magnetic and electric systems together. We'll use the force law approach below, saving the SI approach for a separate paper. What we want to do is find a new dimension for mass M so that instead of (2) we can satisfy (1) with (3) G = 1 We'll call the new thing M prime, to distinguish it from the old symbol for mass. It can be shown that (4) M' = L^3T-2 will satisfy the new relationship from (1) (5) F = M'^2L^-2 as so. (6a) M'LT^-2 = M'^2L^-2 (6b) ML^3T-2 = M'^2 (6c) L^3T-2 = M' -------------------------------------------------------- Comments or criticism gladly accepted. Sincerely, K.
