Page:Annales de mathématiques pures et appliquées, 1814-1815, Tome 5.djvu/28

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24

PROBLÈMES.

Log. des $Sin.$ et $Cos.$ des Long. de la terre, vue du soleil ;

{\begin{array}{llll}\operatorname {Log} .\operatorname {Sin} .\theta &=9,90777605,&\operatorname {Log} .\operatorname {Cos} .\theta &=9,7804949,\\\operatorname {Log} .\operatorname {Sin} .\theta '&=9,9281887,&\operatorname {Log} .\operatorname {Cos} .\theta '&=9,7248022,\\\operatorname {Log} .\operatorname {Sin} .\theta ''&=9,9537546;&\operatorname {Log} .\operatorname {Cos} .\theta ''&=9,6414446.\\\end{array}}

Log. des trois différences Ang. $t,t',h$ et de leur $Sin.$

{\begin{array}{llll}\operatorname {Log} .t&=8,9455031,&\operatorname {Log} .\operatorname {Sin} .t&=8,9449397,\\\operatorname {Log} .t'&=9,0253840,&\operatorname {Log} .\operatorname {Sin} .t'&=9,0245700,\\\operatorname {Log} .h&=9,2883075;&\operatorname {Log} .\operatorname {Sin} .h&=9,2855735.\\\end{array}}

Il en résulte

{\begin{aligned}h\operatorname {Sin} .t\,-t\ \,\operatorname {Sin} .h=&0,0000853,\\h\operatorname {Sin} .t'-t'\operatorname {Sin} .h=&0,0000907;\\\end{aligned}}

On peut donc regarder ces deux différences comme évanouissantes,

Log. des $Cot.$ des trois Lat. Géoc. $B,B',B'',$ et des prod.

\operatorname {Sin} .(\theta -A)\operatorname {Cot} .B,\ldots

;

{\begin{array}{ll}\operatorname {Log} .\operatorname {Cot} .B\ \,=9,8406070,&\operatorname {Log} .\operatorname {Sin} .(\theta \ \,-A\ \,)\operatorname {Cot} .B\ \ =9,8241976,\\\operatorname {Log} .\operatorname {Cot} .B'\,=0,0878113,&\operatorname {Log} .\operatorname {Sin} .(\theta '\,-A'\,)\operatorname {Cot} .B'\,=0,0576892,\\\operatorname {Log} .\operatorname {Cot} .B''=0,2389351,&\operatorname {Log} .\operatorname {Sin} .(\theta ''-A'')\operatorname {Cot} .B''=0,1875247.\\\end{array}}

Log. des prod. désignés par $a,b,c,a',b',c'$ ; (90)

{\begin{array}{llll}\operatorname {Log} .a&=9,6225319,&\operatorname {Log} .a'&=9,7415452,\\\operatorname {Log} .b&=9,8658345,&\operatorname {Log} .b'&=9,9909733,\\\operatorname {Log} .c&=0,0152990;&\operatorname {Log} .c'&=9,1430240.\\\end{array}}

Les produits $a',b',c'$ sont négatifs.

Valeurs des quantités $m,n,o,m',n',o'$ et de leurs logarithmes.

{\begin{array}{llll}m&=-0,3454160,&m'&=-0,3349471,\\n&=-0,6285206,&n'&=-0,6368338,\\o&=-0,2786088,&o'&=-0,3170086.\\\end{array}}