Page:Scientific Papers of Josiah Willard Gibbs - Volume 2.djvu/162

				Number of arc.		Logarithm.						Number of arc.		Logarithm.
$\alpha _{4}$		$-$		1.3181125		0.1199525		$e$		$+$		0.8076104		8.9072019
$\beta _{4}$		$-$		3.930563		9.5944547		$\tan {\tfrac {1}{2}}v_{1}$		$-$		–35° 26' 25''.87		9.8523140
$\gamma _{4}$		$+$		.2326741		9.3667481		$\tan {\tfrac {1}{2}}v_{2}$		$-$		–19° 38' 18''.20		9.5524725
$s_{4}^{2}$		$+$		1.9460513		0.2891543		$\tan {\tfrac {1}{2}}v_{3}$		$-$		–5° 58' 47''.06		8.8424313
$s_{4}$		$+$		1.3950100		0.1445772		$\epsilon$		$+$				9.9648493
$s_{1}$		$+$		1.3309358				$a$		$+$				0.4424586
$s_{3}$		$+$		1.3418749				$b$		$+$				0.4410376
$s_{2}$		$+$		2.2799084		0.3579174		$l$		$-$		.8139130		9.9105780
$s$		$+$		2.4763596		0.3938137		$m$		$+$		.5564152		9.7453990
$s-s_{1}$		$+$		1.1454238		0.0589662		$n$		$+$		.1671768		9.2231760
$s-s_{3}$		$+$		1.1344847		0.0547986		$\lambda$		$-$		.5517065		9.7417081
$S$		$+$		2.0339104		0.3083318		$\mu$		$-$		.8304016		9.9192881
$S-s_{1}$		$+$		.7029746		9.8469397		$\nu$		$+$		.07780215		8.8909916
$S-s_{4}$		$+$		.6389004		9.8054332		$a_{x}$		$-$				0.3530366
$S-s_{3}$		$+$		.6920355		9.8401284		$a_{y}$		$+$				0.1878576
${\mathfrak {S}}_{4}.{\mathfrak {S}}_{2}$[1]		$-$		.0292373		8.4659373		$a_{z}$		$+$				9.6656346
${\mathfrak {S}}_{4}.{\mathfrak {S}}_{2}s_{2}^{2}{-2}$		$-$				7.7501025		$b_{x}$		$-$				.01827457
${\mathfrak {S}}_{4}.{\mathfrak {S}}_{2}s_{2}^{2}{-2}\alpha _{2}$		$-$		.003600696		7.5563864		$b_{y}$		$-$				0.3603257
${\mathfrak {S}}_{4}.{\mathfrak {S}}_{2}s_{2}^{2}{-2}\beta _{2}$		$+$		.012265017		8.0886682		$\tan {\tfrac {1}{2}}E_{1}$		$-$		–33° 16' 50''.08		9.8171633
${\mathfrak {S}}_{4}.{\mathfrak {S}}_{2}s_{2}^{2}{-2}\gamma _{2}$		$+$		.001027926		7.0119616		$\tan {\tfrac {1}{2}}E_{2}$		$-$		–18° 12' 58''.10		9.5173218
$\alpha _{5}$		$-$		1.3145118		0.1187645		$\tan {\tfrac {1}{2}}E_{3}$		$-$		–3° 40' 16''.33		8.8072806
$\beta _{5}$		$-$		.4053213		9.6077994		$k^{-1}a^{\frac {3}{2}}e\sin E_{1}$		$-$		19.85671		1.2979074
$\gamma _{5}$		$+$		.2316462		9.3648252		$k^{-1}a^{\frac {3}{2}}e\sin E_{2}$		$-$		12.85291		1.1090014
$s_{5}^{2}$		$+$		1.9458866		0.2891176		$k^{-1}a^{\frac {3}{2}}E_{1}$		$-$		311.31839		2.4932048
$_{{\text{R}}^{2}}$		$+$				9.0132057		$k^{-1}a^{\frac {3}{2}}E_{2}$		$-$		170.40027		2.2314703
$_{\text{R}}$		$+$				9.5066028		$k^{-1}a^{\frac {3}{2}}E_{3}$		$-$		34.34174		1.538223
$N$		$+$		.14278017		9.1546679		$T_{(1)}$		$+$		296.97504
$p$		$+$		2.7517987		0.4396167		$T_{(2)}$		$+$		296.97447
$\tan {\tfrac {1}{2}}(v_{2}-v_{1})$		$+$		15° 48' 7''.67		9.4518042		$T_{(3)}$		$+$		296.97398
$\tan {\tfrac {1}{2}}(v_{3}-v_{2})$		$+$		15° 39' 31''.14		9.4476366		$T$		$+$		296.97450
$\tan {\tfrac {1}{2}}(v_{3}-v_{1})$		$+$		31° 27' 38''.81		9.7866517
$e\sin {\tfrac {1}{2}}(v_{3}+v_{1})$		$-$				8.7099782
$e\cos {\tfrac {1}{2}}(v_{3}+v_{1})$		$+$				8.7951055
$\tan {\tfrac {1}{2}}(v_{3}+v_{1})$		$-$		39° 25' 12''.94		9.9148727

1. ${\mathfrak {S}}_{4}.{\mathfrak {S}}_{2}=\alpha _{4}\alpha _{2}+\beta _{4}\beta _{2}+\gamma _{4}\gamma _{2}$