D I F 



Conceive a line A B to be the gnomon, A P the shadow, A N the di- 

 rection of the meridian shadow. Draw P N perpendicular to A N, and 

 let A N = .r, P N y> A B = a, I latitude of the place, S = sun's de- 

 clination ; then 



_ (cos. 2 / sin.* 3). A* -f- 2a sin. I cos. I x -f- (sin, a I sin.g S). at. 

 siiPl 



Cor. If cos. = sin. , or I = 90o , the curve is a parabola, if cos. I 

 is greater than sin. , or I less than 90 S, an hyperbola, if cos I is less 

 than sin. 5, or J greater than 90 S, an ellipse. 



DIFFERENTIALS. 



TABLE I. 



Differentiation of Algebraic and Transcendental Functions ; and of th* 

 higher orders of Differentials. 



QUANTITY. DIFFERENTIAL. 



ax ... adx. 



ax+by ~+ e ... adx + bdy A 



dx. 



( m i to \ n 1 / m i ~" 



a + x J n (a -f * 



xy xdg+ydx. 



m n 



* y 



y 



Hyp. log. x ... . 

 Hyp. log. 1 *f * . 



77 E2 



