82
GAUSS AND WEBER ON TERRESTRIAL MAGNETISM.
![{\displaystyle u_{0}-u_{0}'}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1ec298df64939ace0a84616d43f5a7a6684b8401) |
= 23° |
9′
|
![{\displaystyle u_{1}-u_{1}'}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fac29b9b2b27379c7b4f08120a5b7603ad06ee72) |
= 47° |
42′
|
![{\displaystyle u_{2}-u_{2}'}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1fdc914c93226e095973e9ebce94b724a6421c74) |
71° |
48′
|
![{\displaystyle u_{2}''-u_{2}'''}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a9ed3805c32e2c84077c0745bc61c16a232dffdd) |
69° |
21′
|
![{\displaystyle u_{1}''-u_{1}'''}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ce2fb2c6622da994e59f438184566e968cad5470) |
46° |
12′
|
![{\displaystyle u_{0}''-u_{0}'''}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2391bc5ae652b57d4c2193f7db79db43885685fb) |
22° |
27′
|
|
![{\displaystyle R_{0}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9b8916196f182fcbaaca54f931176a4a4f5769cc) |
= 450 |
millimetres
|
![{\displaystyle R_{1}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c1d63c96f59d98589d923c4f0b04222feaa7283e) |
= 350
|
![{\displaystyle R_{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/35f571121c264178676d1df8ab899f238a39bc2c) |
= 300
|
|
|
![{\displaystyle t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560) |
= 6″·67
|
|
|
![{\displaystyle a}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc) |
= 101·0 |
millimetres.
|
![{\displaystyle b}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3) |
= 17·5
|
![{\displaystyle p}](https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36) |
= 142000 |
milligrammes.
|
From these may next be calculated,
![{\displaystyle v_{0}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/60faad24775635f4722ccc438093dbbfe05f34ae) |
= 14(23° 9′ + 22° 27′) |
= 11° 24′·00
|
![{\displaystyle v_{1}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/98d33f5d498d528bd8c10edc8ac8c34347f32b3a) |
= 14(47° 42′ + 46° 12′) |
= 23° 28′·50
|
![{\displaystyle v_{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/eb04c423c2cb809c30cac725befa14ffbf4c85f3) |
= 14(71° 48′ + 69° 21′) |
= 35° 17′·25
|
If now we take the second and the millimetres as the fundamental units of time and space in our calculation, we may deduce from the ascertained values of
,
,
,
,
,
, the following values of
,
,
,
,
, viz.
|
![{\displaystyle {\begin{aligned}A&={\frac {\mathrm {tang} \;11{\mbox{°}}\;24{\mbox{′}}}{450^{3}}}+{\frac {\mathrm {tang} \;23{\mbox{°}}\;28{\mbox{′·}}5}{350^{3}}}+{\frac {\mathrm {tang} \;35{\mbox{°}}\;17{\mbox{′·}}25}{300^{3}}}={\frac {385{\mbox{·}}54}{10^{10}}};\\A^{\prime }&={\frac {\mathrm {tang} \;11{\mbox{°}}\;24{\mbox{′}}}{450^{5}}}+{\frac {\mathrm {tang} \;23{\mbox{°}}\;28{\mbox{′·}}5}{350^{5}}}+{\frac {\mathrm {tang} \;35{\mbox{°}}\;17{\mbox{′·}}25}{300^{5}}}={\frac {384{\mbox{·}}86}{10^{15}}};\\B&={\frac {1}{450^{6}}}+{\frac {1}{350^{6}}}+{\frac {1}{300^{6}}}={\frac {2{\mbox{·}}0362}{10^{15}}};\\B^{\prime }&={\frac {1}{450^{8}}}+{\frac {1}{350^{8}}}+{\frac {1}{300^{8}}}={\frac {2{\mbox{·}}0277}{10^{20}}};\\B^{\prime \prime }&={\frac {1}{450^{10}}}+{\frac {1}{350^{10}}}+{\frac {1}{300^{10}}}={\frac {2{\mbox{·}}0855}{10^{25}}}.\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/009627dd57af44e849cbab8fd5f5ae11314b68a7) | |
From these
is calculated:
|
![{\displaystyle r={\frac {1}{2}}\cdot {\frac {385{\mbox{·}}54+2{\mbox{·}}0855-384{\mbox{·}}86+2{\mbox{·}}0277}{2{\mbox{·}}0362+2{\mbox{·}}0855-(2{\mbox{·}}0277)^{2}}}\cdot 10^{5}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/719ec141f686e108fb5c482bd46ed643458f8366) | |
or
|
![{\displaystyle r=87650000.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d53b0c841e6271847a3ba7ef62b6b1fb66ad00f7) | |