Report of the Gravity Survey Committee. 225 



the iuitijil or final coincidence, foi' tlie method of coincidences is 

 so exact that it may be deemed perfect ; that it is to say any 

 error from this would be swallowed up by much larger errors 

 from other sources ; and that being the case there is a great 

 saving of time in using the model, besides which we are less 

 exposed to errors fiom variations in the clock's rate, changes of 

 temperature, etc. However the actual pendulum might of course 

 be used, and probably in any case an observation or two would 

 be taken with tliis for controul. And besides the saving of time 

 in taking the observations, resulting from using a wooden model, 

 the possibility of taking swings at different pressures in close 

 proximity, merely allowing an interval sufficient to allow the 

 disturbance of temperature consequent on the exhaustion or 

 admission of air to subside, would I think be conducive to 

 accuracy as securing a more near identity in the rate of the 

 clock on the occasion of the two swings that are to be compared. 



You mention the corrections for pressure and temperature. 

 The latter depends partly on the expansion of the metal, partly 

 on the effect of temperature in altering the state of the air, and 

 therewith the correction on account of the air. I am not sure 

 whether or not you meant to include the effect of the expansion 

 of the metal. 



If it is intended to keep the two parts separate, I suppose it is 

 meant to calculate the part due to the metal from the linear 

 expansion either ascertained by direct observation or assumed as 

 known for the kind of metal employed. As to the air, the 

 correction for buoyancy, and that portion of the correction for 

 inertia which would form the whole if there were no viscosity, 

 both one and the other vary as the density, and therefore in a 

 known manner as regards the temperature. The rest of the 

 correction for inertia depends in a more com[)licated manner on 

 the temperature. The whole of this residue for a sphere, and the 

 first term and most important part of it for a iiot too narrow 

 cylindrical rod, varies as \/7jip. p of course varies inversely as 

 \-\-a6 {9 the temp, a the co-efft. of expansion) but /x increases as 

 the temperature rises, according to what law does not appear to 

 be known for certain. T think experiments on transpiration gave 

 it about as (l + a^)''' but I am away from books of reference, 

 and I do not remember exactly. 



Q 



