520 BELL SYSTEM TECHNICAL JOURNAL 



The changes in t and g are quite independent of each other and so can be 

 treated separately. Other factors that will be described also affect the 

 rate, and it is the object in every precision clock design to reduce such 

 variable effects to the absolute minimum. 



Some control can be exercised over every factor except g, which remains 

 a property of space and is dependent only on the proximity of matter and 

 on acceleration. As is well known, the value of g varies over the surface of 

 the earth due chiefly to its deviation from spherical shape, and because of 

 the uneven distribution of matter. It also varies with vertical displacement 

 or tides at any location to such an extent that a gravity clock that keeps 

 accurate time at ground level will lose a second a day or more in a tall 

 building. Actually, it is now possible to chart variations in g with high 

 precision through measurement of the rate of a pendulum clock against a 

 standard whose rate does not depend upon gravity. 



Most of the factors that can affect I have been studied critically and 

 means have been found to reduce them to very small effects. The chief 

 source of variation was at first the temperature coefficient of the pendulum 

 rod. With ordinary metals the rod expands from 10 to 16 parts in a million 

 per degree C, causing a proportionate change in rate of half this amount, 

 corresponding to from one-half to two-thirds of a second per day. Many 

 ingenious means were developed to reduce this effect, starting with George 

 Graham's mercury-filled bob in 1721, followed by John Harrison's grid-iron 

 pendulum in 1726, and a great number of variations on these ideas, all de- 

 pending on the differential coefficient of expansion of dissimilar materials. 



About the year 1895, Charles Edouard Guillaume of Paris developed an 

 alloy, consisting chiefly of nickel and iron, which he called Invar, because 

 it had a very small temperature coefficient of expansion, from which pen- 

 dulum rods could be made. The use of this material made it unnecessary 

 to resort to complex compensated pendulums with their own inherent insta- 

 bilities, and the accuracy of timekeeping was increased another step. The 

 residual temperature effects could be measured readily, and compensated 

 if desired, by the use of a small bar of aluminum attached to the bob. 



Some other important factors that affect the working length of a pendu- 

 lum are the aging of the supporting rod, the "knife edge" or spring used 

 for the suspension, the nature of the main supporting column or frame, 

 and some atmospheric effects caused by changing temperature and pressure. 

 In the most accurate pendulum clocks, the atmospheric effects are greatly 

 reduced by mounting the pendulum in partially evacuated, hermetically 

 sealed enclosures which can be temperature controlled. All of these factors 

 and many others are discussed in every good treatise on accurate pendulum 

 clocks. They are mentioned here chiefly for the purpose of comparison 

 with like factors in the quartz crystal clock and to show how in many 



