418 Mr DENISON, ON SOME RECENT 



relation to each other, but depend on the accidental state of the friction in different parts of 

 the clock, and upon the construction of each individual escapement. And it is by no means 

 an unimportant circumstance, that such accuracy as can be obtained in a clock of this kind 

 depends very much upon the amount of skill and care which have been employed in its con- 

 struction. In the best clocks the pallets are jewelled, the pivots turned as small as possible, 

 the wheels and pinions made with very high numbers of teeth, and various other refinements 

 are introduced, because the clockmakers have long ago found out that nothing like accuracy 

 of performance can be obtained, except by reducing all the friction to the lowest possible 

 amount. The consequence is that such clocks are very expensive, costing from £30 to ^80, 

 according to the degree of finish, though they contain very little machinery, and that of an 

 extremely simple kind. For though it may be theoretically true that the friction on the dead 

 part of the pallets (called for shortness the 'dead friction') does not directly affect the time of 

 vibration, yet if you try the experiment of artificially thickening the oil there by putting a 

 little resin to it (you may clean it off again with spirits of turpentine), you will find that the 

 friction does in practice affect the time of vibration very sensibly by altering the arc, on several 

 functions of which the time depends. 



One of those functions is the circular error (as far as it is uncorrected by the pendulum- 

 spring, and how far that is is very uncertain), and this tends to make the clock gain if the 

 arc is diminished. But, on the other hand, there appears in the expression for the daily rate 

 another term involving da, or the variation of the arc, and of the opposite sign to the circular 

 error. And I have found, both from previous experience, and from some experiments expressly 

 made for the purpose of testing the value of an invention which professed to make a pendulum 

 with a dead escapement always isochronous, that sometimes one of these terms may prepon- 

 derate, and sometimes the other. There is, besides, another term in the expression, depending 

 on the variation of force of the impulse, independently of the variation of the arc. And it 

 appears that when a decrease of arc arises chiefly from an increase of friction on the pallets, 

 the clock will generally lose in spite of the circular error ; but where it arises chiefly from an 

 increase of friction in the train the clock will gain. But at any rate the amount of the 

 increase or decrease of time which may be expected to accompany any given increase or 

 decrease of arc, arising in the natural state of things, is quite uncertain. And therefore (if 

 not for other reasons) all such things as cycloidal checks, springs for accelerating the pendu- 

 lum as the arc increases, and any other 'isochronous' contrivances, are practically useless, and 

 in manv cases are even more likely to aggravate the actual error of the clock than to correct it, 

 however well they may appear to answer in arbitrary experiments for producing some enormous 

 developement of one of the errors without taking any notice of another, which in the natural 

 state of things may be much larger in an opposite direction. 



The only exception to this remark is that, in turret-clocks, in which the variations of 

 friction are much greater than in regulators, it seems to be found beneficial to give a very 

 slight recoil to the dead part of the pallets. But I suspect that the advantage is not so much 

 in the accelerative effect thereby produced, as in the tendency of such a recoil to check the 

 variations of the arc, by the increased friction which it opposes to any increased swing of the 

 pendulum. The most valuable addition however to a turret-clock for the purpose of equal- 



