106 Description of a Mercurial Pendulum. 



« C* = 6-4 x6-4 = 40-96, 3g= 107-4 -^ = 9-6; therefore, 



3„^ + 3»r+r^ = 1 17)4573-24(39-0S753 for the distance of cen- 

 3(7 + -^ tre of oscillation for 30° of the thermometer. 



" If 10 inches of steel with 60^ expand 0-0038, then 42-2 will 

 expand 0-0160; therefore 42-2 + 0-0160 = 42-2160 = C D. If 

 10 inches quicksilver expand 0-0519, 6-4 gives 0o332, and 

 6-4 + 0-0332 = 6-4332 = c. Hence 42-2160 - 6-4332 = 

 35-7828 = a. And from these numhers tlie centre of oscillation 

 is found as above =39-08782 at 90° of thermometer; which dif- 

 fers from the former deduction, or when the thermometer stood 

 at 32°, only 000029. 



" It is well known that when the ball of a pendulum is let down 

 0-01 of an inch, it will go 10 seconds slower in 24 hours; and 

 therefore 0-001 will l)e equal one second, and O'OOOl equal ~ of a 

 second in 24 hours. It follows from this, that the above pendulum is 

 so nearly corrected, that its daily rate at 90° of thermometer would 

 be nearly 0-"29 slower than at 30", and that the correcting co- 

 lumn is rather too short; but the glass cistern itself expands the 

 same wav as the quicksilver, and the excess of its height above 

 the top of the included mercury will fullv compensate the error 

 of 0-"00029. It likewise follows that the steel rod 42-2 inch, 

 being lengthened 0-0160, it would (if there were no compensa- 

 tion from the quicksilver) go 16" slower at 90° than at 30" of the 

 thermometer. But since 6-4 inches of quicksilver compensates 

 this, fV of an inch will compensate one second. For if the pen- 

 dulum went one second slower in 24 hours at 90° than at 30° of the 

 thermometer, the remedy would be to add -^^ of an inch more 

 quicksilver. A glass cistern 2 inches diameter inside, and filled 

 with quicksilver to 6-4 inches will contain 10 pounds weight very 

 nearly, and therefore 6*4 inches give 10 lbs. or 160 ounces, /q- of 

 an inch gives 24 ozs. that is one ounce of quicksilver added or 

 subtracted will verv nearly compensate 0-"l of the variation of 

 the daily rate at 30' and 90° of the thermometer. 



" There are five other things that ought to be particularly at- 

 tended to in constructing a pendulum of this sort, which are not 

 deduced from theory, but the results of 4 years experience. 



" 1st. The spring at top should be one inch long, and of a pro- 

 per stiffness. 



" 2d. Let the crutch have a steel fork to embrace the steel rod 

 at 7 inches from C, the point of suspension, and be free, with as 

 little shake as possible. 



" 3d. Let a scale of inches and tenths be placed at 44 inches 

 from C, for the purpose of determining the arc of vibration and 



olso 



