Practical Thermometric Standard. 543 



by using the bulbs themselves as compensated mercury weight- 

 thermometers. These observations were exceedingly con- 

 sistent, and could be repeated with great precision ; but they 

 could not be made to give at all a reasonable result either at 

 the S. B.P. or between 0° and L00°, when reduced by any of 

 the various formula? which have been derived from Regnault's 

 experiments on the absolute expansion of mercury. Within 

 the limits of uncertainty of the expansion of the bulb, the 

 results of this series of experiments agreed perfectly with our 

 previous work ; but extrapolation to 445° appeared extra- 

 vagant, and even between the limits 0° and 100° it seemed 

 useless to attempt to proceed to a higher order of accuracy 

 until the fundamental question of the absolute expansion of 

 mercury had been settled. The order of uncertainty involved 

 in observing the linear expansion and deducing the cubical 

 coefficient appeared to be of a similar magnitude. We 

 therefore decided to postpone further experiments until this 

 point could be cleared up. It appeared to me that it would 

 be possible, by using longer columns of mercury, and by ob- 

 serving the mean temperatures of the columns with long 

 platinum-thermometers, to secure a higher order of accuracy 

 than had been attained by Regnault. My experiments in 

 this direction were delayed by my removal to Canada, and 

 by the work of fitting up the new laboratory at McGill Col- 

 lege; but since my return to England I have secured a suitable 

 site for the work, and have made preparations which I hope 

 soon to be able to complete. The deviations of the platinum- 

 thermometer from the parabolic formula are of the same order 

 as the uncertainty of the expansion correction. We may well, 

 therefore, be content to assume the simple parabolic formula 

 for the present, and leave the small corrections to be deter- 

 mined by a later approximation. 



As an illustration of the extent to which the value of the 

 S. B.P. is affected by the uncertainty of the expansion cor- 

 rection, the following values of the correction at 445° and 

 1000 c O.j according to the formulae employed by recent ob- 

 servers, may be interesting and instructive. It is usual to 

 assume that the expansion may be represented over a moderate 

 range of temperature with sufficient accuracy by a formula 

 of the type v/v = 1 + at + bf 2 , where t is the temperature on 

 the centigrade scale. The value of the fundamental co- 

 efficient c (the mean coefficient between 0° and 100° C.) is 

 evidently (a+ 100 b). If the temperature t on the centigrade 

 scale were calculated on the assumption that the bulb did 

 not expand at all, the values would all be too low except 

 between 0° and 100° C. The correction to be added to the 



