TaMe contains the declination of the body from 1 to 3'2, and at the top 

 of each succeeding column is set down the latitude of the place from 50 

 to 60 both inclusive. 



For the sun, the arc gives the time of its setting-, and if it be subtract- 

 ed from twelve o'clock, you get the time of its rising. 



For a star, add and subtract the equation to and from the time at which 

 the star passes the meridian, and you have the time of its setting and 

 rising. 



The time so given is the hour when the centre of the sun appears in the 

 horizon, the eye being at the surface of the earth ; thereby taking into 

 consideration the effect of refraction. 



Example. In latitude 5-2. 12'., and declination of the stm 23. 28'., 

 what is the time of its rising and setting ? 



h. m. 



Latitude 520. declination 230 arc 8. 1(> 



53. arc 8. 22 



i (j 



Hence lo : 12' :: 6m : Im, to be added to 87/. 16m. h. m. 



Latitude 52, declination 23..... arc 8. 16 



24 arc 8. 24 



1 8 



Hence 1 : 28' :: 8m : 4m, to be added also to 8A. l&m. 

 Therefore the semi-diurnal arc 8h. l&m. -f- \m. 4. \m. 8/i. 21 w. the 

 time of setting; and 3h. 39/. time of rising. 



AREAS of Currcs, whoso Equations are given. 

 Let r and y be the ^abscissa and ordiiiate of the curve, then 



Area fl. ydx, 



Ex. \. Area of a triangle rr base X i perpendicular. 

 2. Area of the common parabola = % xy =. of the circumscribing 



it-i n 

 rectangle. Or if the general equation is a x y , area rr X 



.r y. 

 8. Area of circle whose radius 1 is 3. 14159 &c. or if rad. r, and 



^ ~ ,'i. 14159 &c. area = x r~ ; or in terms of circumference C = C. . 

 1. Area of ellipse, if a and b = -* ax. maj. and min., = T. u //. 

 5. Area of cycloid 3 times area of the. i^eucratiu^ <-irclc. 

 28 



