773 



AZIMUTH DIAL. 



and from o to N in tangents of the sun's declination, from zero to 234 

 degrees, the radius of the circle being equal to the eccentricity of the 

 ellipse. To these graduations are annexed as many corresponding days 

 of the month as can be introduced. 



In order to investigate the place of any hour-point, as R, let A be 

 the foot of the stile for any given day. Then AK will be the direction 

 of the shadow for the given hour; and there must be found the 

 azirnuthal angle MAR, or its supplement M A R'. Now the sun being 

 in the plane of the hour-circle which cuts the horizon in R A R', and it 

 being understood that, in the celestial sphere, there may exist a 

 spherical triangle formed by arcs joining p the pole of the equator, 

 s the place of the sun, and z the zenith of the place, or the point 

 vertically above o [see fig. to AZIMUTH, and imagine s to be put in 

 place of ], we shall have PZ the co-latitude of the place, PS the sun's 

 north-polar distance, and the given hour-angle at P ; to find the angle 

 at z ( = MAR' or MAR). 



In that triangle we obtain [SPHERICAL TRIGONOMETRY, formula 6], 



cotan z = 



cos z P cos p cotan p s sin z p 



sin p 



But RB (fig. above) being let fall perpendicularly on on produced if 

 necessary, let OB=a:, BR=y, o\=x > ; then 



cotan MAR ( = cotan z) = =^H 

 BR y 



Equating these values of cotan z, there is obtained x'= 

 x sin P y cos z P cos p + y sin ZP cotan PS 



sin p 



This equation containing three unknown quantities, the problem is 

 indeterminate ; but, since the following conditions must be satisfied, 

 the values of x and y may be found : First, the position of R, the 

 hour-point, must be independent of the sun's polar distance ; therefore 

 x and y must be independent of PS, which gives 



x sin p y cos zp cos P=0; 

 also x 1 must be independent of the given hour ; whence ?^5 must 



sin p 



be considered as constant; let the constant be represented by m; 

 then 



and x' = m cotan pg. 



AZULMIC ACID. 771 



From the equation for we have 



x=y cos ZP cotan p, 

 and substituting the value of y, 



x=m cotau ZP cos p. 



Squaring the values of x and y, and adding the results together, 

 there is obtained, after reduction, 



a? y* 



m 5 cotan 2 z p m* cosec 2 z p ~~ ' 



which is the equation to an ellipse, having for its semi-tranverse a*i 

 m cosec ZP, and for its semi-conjugate axis m cotan ZP. 



The constant m may be taken of any magnitude at pleasure according 

 to the intended scale of the dial ; thus the ellipse may be traced. The 

 hour-points may be found by giving to the angle P successive values, 

 as 15, 30, &c., and corresponding values for the half-hours, quarter- 

 hours, &c. in the above values of x and y. 



AZOBENZIDE (C,,,H 10 N.,). A reddish-yellow crystalline body, ob- 

 tained along with aniline, by the dry distillation of azoxibenzide. It is 

 lightly soluble in water, and easily soluble in alcohol, fuses at 149" 

 Fahrenheit, and distils without alteration at 379. 



AZOBENZOYL (C M H 15 N S ). An unimportant neutral solid, obtained 

 amongst other compounds by the action of ammonia on oil of bitter 

 almonds. 



AZOERYTHRIN. [LICHENS, COLOURING MATTERS OF.] 



AZOLEIC ACID. One of the acids formed by the action of nitric 

 acid on oleic acid. 



AZOLITMIN. [LICHENS, COLOURING MATTERS OF.] 



AZOMARIC ACID (C <0 H 2 .(N0 1 ),0 8 ) ? A yellow, amorphous acid, 

 obtained by acting upon resin with a large quantity of nitric acid. 



AZONAPHTYLAMINE. [NAPHTHALIN.] 



AZOTANE. [NITROGEN, CHLORIDE or.] 



AZOTE. [NITROGEN.] 



AZOTIC ACID. [NITRIC ACID.] 



AZOXIBENZIDE (C^H^N.O,). A yellow, crystalline, inodorous, 

 and tasteless substance, obtained by the action of caustic potash upon 

 an alcoholic solution of nitrobenzol. 



AZULMIC ACID. This name has been applied to the brown 

 flocculent matter which is deposited when an aqueous solution of 

 cyanogen is exposed to light. 



