102 Mr. Davies Gilbert on the 



a; — — _i_ and y =: a — a—b . x, consequently, the 



a— b a — b 



fluxion of the variable circular excess — (a — a — b . xY X x 



16 ^ 



the fluent of which is — (a"x — ax a—b .x^ + " ~"" x^) 

 16 ^ -3— 



when X = 1 equal to — ^^+^:^+^\ ^l,ich multiplied by 



the number of seconds observed between the arcs a and b, will 

 give the whole circular excess in seconds. 



And here it may be remarked that the expression 



a' y. ab X b'' j •. i. . j *i 

 ; corresponds, as it ought to do on the supposi- 

 tion, with that for measuring the frustum of a pyramid. 



A formula involving both these causes would be extremely 

 complicated if, indeed, the fluent could be assigned in finite 

 terms. But it is probable that by carefully noticing the varia- 

 ble circular excess between two very small arcs, and between 

 two others comparatively large, some estimate may be formed 

 of the relative magnitudes of the retarding powers exerted by 

 friction, and by the resisting medium, unless the former should 

 really be found inappreciable in all practical cases. 



A Table for correcting the Time, as shewn by a clock, having 

 a brass weight, or ball, to its pendulum, for the variation of 

 one inch in the height of the barometer. 



Arguments. — The time elapsed since the last observation 

 of the barometer. 



And the present observed height ^ 30 inches ± — the vari- 

 ation between the observations — 



Additive, if the sum is Plus. 



Subtraclive, if it is Minus. 



