B 



I ! 



Description of a Mercurial Penduhim. 105 



for wliich purpose a thermometer of white flint glass q 

 with a large bulb and long stem was filled to the top 

 when the temperature was precisely 32°; it was then 

 put into steam of 212°, and the quantity of quicksilver 

 that ran over was weighed ; the result was that 10000 

 grains gave 155*4S grs. that expanded or run over. 

 This is the excess or difference between the expansion 

 of the quicksilver and glass, and from which the fol- 

 lowing conclusion is drawn : That a cylinder of white 

 flint glass filled at 32° of the thermometer with quick- 

 silver to the height of 10000 inches, at 2 12" the column 

 of quicksilver would be 10155-48 inches long. 



" As 10000: 155-48 : : 10 inches : 0-15548 for a 

 difference of heat = 180°; and therefore 10 inches for 

 a difference of heat =60", will give 0*05 U) very nearly. 



" From the above data the calculation and construc- 

 tion of a mercurial pendulum is easy. Let C B D re- 

 present such a one, having the rod and frame at bot- 

 tom of steel, and a white-flint glass cylinder resting on 

 the bottom of the frame, and filled with quicksilver to 

 such a height, DB, that its expansion (which is up- 

 wards) shall be somewhat more than double the ex- 



pansion of the whole rod from C to D. Suppose then D 

 that C D is 42 inches : then as 10 inciies steel : : 0-0033 : : 42 

 inches to .. .. .. .. ., 0-01596 



2 



The expansion of the quicksilver nearly = 0-03192 

 But 0-0519 inch comes from 10 inches of quicksilver, therefore 

 003 192 will come from 6-2 inches, which is nearlv the height of 

 the column ; add ^y of 6-2 inches to the column, or 0-2 + 6-2 = 

 G'4 inches, which is very nearlv the length of the column. Let 

 CD = 42-2 inches, then CD- 6-4 = '35-S C B. 



"PutCB= a =35-8, BD = c6-4. To find the centre of os- 

 cillation 0, or its distance from C. Tiie formula is C © = 



3a + — 

 ■I 



" Let us suppose then, that the pendulum, having C B and 



B D of the above dimensions, is constructed and set a-going at 



30° of Fahrenheit: it is required to find, 



" 1st. The centre of oscillation. 



" 2d. To find it a second time when the thermometer is at 90" 



and CD and BD expand with 60" of heat. 



" 3fl«=35-8 x35-Sx3 = 3844-92, 3flc = 35-8 ?<0-4 x3 = 



687-36. 



" C*= 



