666 ME. C. W. SIEMENS ON UNIFOEM ROTATION, 



and in substituting this value for h! in the first formula, we have 



2nr ' 



or 



2rT ' • • • • ^' ; 



for our corrected formula to determine the velocity of cup with continuous oversow. 



In applying this formula to the clock, taking for § its value of 8 millims. and the 

 other values also in millimetres in order to avoid fractions, we find 



19600 X 38 A + TjrTr^^TTT^^ 

 , \ 400-16-05/ » A 1 .- 



n'=- ^^^ =7'4 revolutions per second, 



or '1 revolution per second less than the actual speed. This remaining excess of the 

 actual over the calculated velocity of the cup is rather more than what may be fairly 

 attributed to error of measurements, and appears to be due to adhesion of a film of liquid 

 (which may be estimated at nearly "25 millimetre thickness) to the inner sides and edge 

 of the cup, whereby its effectual dimensions are proportionately reduced. For a uni- 

 form speed this error must be a constant quantity, which cannot affect the working of 

 the instrument injuriously, so long as the other conditions are such as to produce uniform 

 rotation. The discrepancy is diminished by increasing the dimensions of the cup, and 

 its amount is such that the compensation is effected, under all circumstances, by one or 

 two turns of the regulating screw supporting the vertical spindle. 



When the regulation of the cup is once effected, it continues to rotate at a remarkably 

 uniform rate. Change of temperature affects the density of the liquid considerably, but 

 does not influence the rate of the cup otherwise than inasmuch as it affects the level in 

 the cup-chamber, rising vnth increase of temperature proportionately to the depth 

 of liquid it contains, which change is inconsiderable. The lineal dimensions of the 

 cup, and the length of the suspending spring, will also increase, all tending to lower the 

 rate with increase of temperature; but, on the other hand, the length of the upright 

 cup-spindle increases with increase of temperature, and by regulating the length and 

 composition of that spindle properly, entire compensation for change of temperatm-e is 

 effected. The cup-chamber being entirely closed against the atmosphere, no fault can 

 arise through evaporation or dispersion of the liquid within moderate periods of time. 



In the case of the clock under consideration, no compensation for change of tempera- 

 ture was provided, nor is the cup entirely balanced by the spring, yet its rate is as uniform 

 as that of the common clock with which it has been compared ; but in order to test the 

 regulating-power of the instrument, the driving-power was varied by the introduction of 

 artificial resistances into the galvanic circuit, when the following resultswere observed: — 



