1 fr - -. 



Rev. C tS. Lyman on the Pendulum Exp 



413 



•i. 



with the arrow parallel to it is slid around the surface so as to 

 make the cone gradually more steep, it will be seen that the an- 

 gle of inclination which the first arrow forms with each succes- 

 sive arrow that it meets, is continually increasing, and is precise- 

 ly equal to the portion of the original circle that has been covered 

 up by the over-lapping of the sides. Let the edge overlap for 

 example one quarter of the circle, or cut off 90°, the cone will 

 then be as in the accompanying figure. 

 ^ All but 270^ of the en- 

 tire circle are seen to be 

 concealed ; the figures on 

 the margin representing 

 not the angles made by 

 the radii on the present 

 circle, but on the original 

 one. But these 270 ori- 

 ginal degrees are made to 

 encompass the entire base, 

 or to equal the entire cir- 

 cle of latitude to which 

 the base of the cone cor- 

 responds. Instead of 12 

 radii to the circle, as at 

 firstj there are but nine 

 of the 12 left; hence 

 each pair of radii, instead of including only 30 degrees of a 



12 



circle of latitude, includes 30^X— ==40^; and the angles which 



the arrows make with the successive radii, viz., 30, CO, 90, 6cc. 

 degrees are continually falling short of the corresponding angular 

 motion of the earth, viz., 40, 80, 120, &c. degrees, so that when 

 a complete circuit of the earth has been made, or 360°, the ar- 

 rows have changed their relative direction only 270°, or fall 90 

 short of making an entire revolution in 24 hours, as will be seen 



i 



in the figure. 



270 



24 



gives 11° 15' for the motion of the plane of 



vibration per hour in the latitude contemplated. And as this lati- 

 tude must be that, the entire circle of which is just fths of the 

 circle which has the slant height of the cone for radms as ap- 

 pears from our first figure, it follows that the sine of the latitude 

 must be just |ths of radius, or the latitude 48° 35' 25". VVhen 

 the sides of the paper are lapped so that 180° of the circle are 

 concealed, the first arrow will be found to be parallel to that at 

 the 180th degree, but pointing in an opposite direction, having 

 performed half a revolution during an entire revolution ot the 

 earth. The base of the cone, beinfe now just half its original 

 periphery and diameter, corresponds to a latitude the sme of 



SEco>Ti Semes, VoL XII, ^"o. 36.-^07., 1851. 53 



' * 



