623.] These fifteen equations are not independent, and in order to deduce the dimensions of the twelve units involved, we require one additional equation. If, however, we take either or as an independent unit, we can deduce the dimensions of the rest in terms of either of these.
(1)
.
(2)
.
(3) and (5)
.
(4) and (6)
.
(7)
.
(8)
.
(9)
.
(10)
.
(11)
.
(12)
.
624.] The relations of the first ten of these quantities may be exhibited by means of the following arrangement:
,
,
,
and .
,
and .
and ,
,
,
.
and
,
,
.
The quantities in the first line are derived from by the same operations as the corresponding quantities in the second line are derived from . It will be seen that the order of the quantities in the first line is exactly the reverse of the order in the second line. The first four of each line have the first symbol in the numerator. The second four in each line have it in the denominator.
All the relations given above are true whatever system of units we adopt.
625.] The only systems of any scientific value are the electrostatic and the electromagnetic system. The electrostatic system is
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![{\displaystyle [{\mathfrak {B}}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/44189f0ca3781ee357f707d08fd9750288555656)
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![{\displaystyle [{\mathfrak {H}}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/655e2f26a404f5eb0983b3767b6a1b786809d0b3)
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![{\displaystyle [{\mathfrak {C}}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0b13358d8886deebd51ae588ea9ac1679a1836ea)
![{\displaystyle {}=\left[{\frac {e}{L^{2}T}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/75683fca09b9f015745f531455a219e215f751bc)
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![{\displaystyle [{\mathfrak {A}}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/51f834b7a6573caba9cd118db07818de31641cf4)
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![{\displaystyle {}=\left[{\frac {m}{L}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b0ba43c611dbe3f38c75cfb1af01731c97382719)
