Page:Encyclopædia Britannica, Ninth Edition, v. 6.djvu/213

Rh COMET 185 The calculation of M = ^-, is as follows, by (II.) : Log. tan.. 0&quot;.. . + 0-3232781 Log. tan. &quot;... + 5509163 And thus substituting logarithms in the factors for p and p 2, our equations stand thus, in the form for proceeding with the work Log. sin.(a&quot;-A&quot;;...-a-3644U No&amp;lt; 3 + 3 5556279 r- 0-969880 - [0 2296858], p + [0 4944306] p 2 r &quot;i o 966903 JO 63335701 a + [0 4748536] p 2 . ^ S ^-&quot;o&quot;.o8S^2 Log. m...- 0-4867341 Log. sin. (a -A )...- 9 8083o92 ^ ^ ((/ ,, A } .. _ 9 . 8988S64 k* = 0-109114 - [9 -261 2653] . p + [9 5408186] p 2 We have now to find the value of p by trial and error. Here, if k 3 = F + G . p + Hp 2, we have F 0-10911 loo- G 9-26127 log II +9-54082 + 0-2955933 + 0-JWSMOS No. 1 + 1-975119 ,9.1900117 Log. tan. (8 .. . + 0-1633710 . . jf 3 NO 4 + 1&quot;1257162 And for a first approximate value of p, by (IV.), No. 2 + 1-456703 No. 1-No. 2 + 0-518416 T LJJ- // &quot; t ff *09071 7 Log. F... -9-03788 Log. 2 ...= 0-30103 Log.H...=9 54082 Log. H... = +9-54082 Log... . + 9 / 146784 Loe. (&quot;- )... 0-9739822 fr.fr CVn ^ TSTn 4^ 4- 0^1 49SQ -^ u o- V&quot; 9-49706 Log. 2H...= + 9-84185 / .. i&quot;^ Q. A oo(Qx T ._ I l &quot; G 0067305 /&quot;/&quot; /&quot; ~*J og-V TT-&quot; y /*oOO -0*58058 i / i (VAftfiT^o^ Log. tan. ivj,... 0-06370 Log. / y/^-... + 9 -74856 M... 9.6699800 Log. p ..._^8122G tan.^...- 0-83202 3P... 9-3399600 &quot; &quot; C49 *... 9822 .5 Next, we form the equations (III.) for the determination of r&quot; 2, r &quot; 2 , and /c 2 by successive assumptions for the value of p , Log. R 9 -9933590 Log. R &quot; 9 9926916 44-... 4911 ,25 In the earlier approximations we may use five-figure logarithms. With p = 649, the work proceeds thus Log. p 9-81224 Log. p 2 ...9 62448 -0-22969 +0-49443 R 2 =. 96988 Loo-, p .... 9-81224 Log. p 2 9 62448 No. (2.).. .. + 1-31494 Log. R 2 9 9867180 Log. R &quot; 2 99853832 R 2 0-969880 R &quot; 2 966903 Log. 2 G 3010300 Log. 2 0.3010300 Log. R 9-9933590 Log. R &quot; 9 9926916 Log. cos. (a -A )... 9-9352968 Log. M 9 6699800 (1) -0-04193 (2.) + 0-11891 +2 28482 TLT t /i i -i m T; 9-636 +0-47185 No. (1.).... 110135 Locr. p 9-81224 Log. p 2 9 62448 r 2 .... 1-18347 ( 3..... 0-41560 (4.) + 0-09933 *** *&quot; ^^ 0-2296853 L g &quot; C S &quot; ( &quot; &quot; A } &quot; 9 CG% ^ 4 &amp;gt;j ~r. KQ - MK 9-6333570 JNo 1 69/015 No. 0-429890 Log. sec. 3 0-2472153 ===== LOJT r 0-03653 -9-26127 +9-54082 Log. p 9-81224 Log. p 2 9 62448 Log. sec. /3 2 0-4944306 T ncr cop fl &quot;2 1 - lS48Q^fi (5.) -9-07351 (6.) .... + 9-16530 M- rt -U^-IOIQtJ^ -&quot;-&quot;OS- SeC &quot; P No. (6.) +0-14632 y^^ + i^ M 9 3399600 0-4748536 Constant... + 0-10911 No. (5.) -2-mf4 No.(3.)....-0-27900 No + 2-984376 Therefore the equations for r 2 and r &quot; 2 are .ji r, .onajn i fiQTfii?; o_ I-IOIOQ^ v2 F + n. 1? oo * i &quot; ! 94487 Log. *.. +9-13669 L - r - Z r &quot; 2 = 0-966903 - 0-429890. p + 2 9S4376. p 2 Log. ^... + 9-56835 L - r &quot; l r 2 + r &quot; 2 = 1-936783 - 2 -1 26905. p + 6 106359. p 2 Log. 2 0-3010300 Log. 2 3010300 Log. R 9-9933590 Log. M 9 6699800 Log. R &quot; 9-9926916 Log. cos. (a &quot;- a )... +9 9899024 k... 0-37012 r .... 1-08788 /I-&quot; 1 ^0-ifiO 17,&quot; O lR^Oft J(r + r&quot; )... 1-24124 P 0-18506 Log. cos. (A &quot;- A ).. + 9 9748170 +9-9^94 B-i( r +r &quot;) + |/fc 1-42630 020189/6 No R 4-0-913990. Constant 1-43781 Constant 1 &quot;43781 V o PJ i 1 .Q07^i?n Log. 2 D 8010300 I of B 15421 Log D 02373 Log. 2 0-3010300 Log. M 9 6699800 Log. R &quot; 9-9926916 Log. tan. /8 +0 1633710 Log. cos. (a - A &quot;) ..+ 9 -8096060 Log. tan. 3 &quot; + 55091 63 iLo&quot; B 07711 iLog. D 0-01187 Lo J, ... 1-66913 Log. z&quot; 1-47341 + 0-1033276 +0-6852973 sf 46-6800 2&quot; 29-7447 No. 6 + 1-268608 No. 9 + 4-845039 ^g- 2 0-3010300 No. 8 + No. 9 + 5 758968 T.ncr M Q 66 QQ 800 z 1 zf 16 &quot;9353 (t &quot;-t } 18-9841 Log. R 9-9933590 Log. cos. (o &quot;- A )... + 9 -8654465 Error . . - 2 0488 If for a second approximation we take p = 7139, and calculate z - z&quot; precisely as before, the error in the interval from the first to the third observation, or (t &quot; t ), is found to be - O d 360G, which, compared with the error of the first assumption ( - 2 d 048&), shows a change of + l d- 6882 for an increase of - OG49 in p; or of ^th part, and by mere proportion we have p = 72776, for a third approxi mation, giving the error in interval = + O d- 0222, so that we are now approaching the true value, and with VI. 24 + 9-8298155 No. 7 +0-675796 No. 6 + No. 7 + 1-944404 So that the equation for F is thus formed, /a + *&amp;gt;&quot;) - 1-936783 - 2 126905.p + 6 106359.p 2 -1-827669 + l-944404.o - 575S968.o 2 k- = 0-109114 - 0-lS2501.o + 347391. p 2