366 THE SCIENTIFIC PAPERS OP 



under this changed condition of equilibrium will, however, not 

 become shortened, as in the case of the barometer when affected 

 by a diminution of atmospheric pressure, or as was the case in the 

 instrument before described, but for every fraction of a millimetre 

 which the top level rises the centre of the diaphragm will rise 

 also, and in an increased ratio, depending upon the proportion 

 of the diameter of the solid central portion of the diaphragm 

 to the diameter of the cup. If the central solid part of the 

 diaphragm was only a point, it is easy to see that for every 

 fractional rise of the mercury in the upper cup the centre of the 

 diaphragm would rise three similar fractions, and the real height 

 of the mercury column would diminish two fractions instead of 

 increasing one. But in reality the central portion of the 

 diaphragm is so proportioned to the cup, that for a rise of one 

 increment of height of mercury the centre of the diaphragm would 

 rise to about double that amount, and the effectual height of the 

 mercury column would decrease instead of increasing to the amount 

 of readjustment required. If the elastic range of the springs 

 balancing the pressure of the mercury were equal to the height of 

 the mercury column, the increase of height on the one hand would 

 be exactly balanced by the increase of elastic force on the other, 

 and the instrument would be in a condition of unstable equilibrium, 

 similar to that of a balance-lever suspended at its centre of 

 gravity. If, on the other hand, the elastic range of the springs 

 were equal to one half the height of column, the increase of elastic 

 force would proceed at double the rate of the increase of potential 

 of the column, and the result would be a scale proportionate to the 

 simple height of column. 



It follows from this that the elastic range of the springs must 

 be less than the length of the mercury column. In the actual 

 instrument the elastic range of the spring exceeds to some extent 

 half the length of the column, so that one division of the instru- 

 ment represents less than its seeming proportion of the total 

 gravitation. It would be difficult to determine the actual scale of 

 the instrument d priori and I therefore adopted the easier and 

 safer method of relying for its final adjustment upon the result of 

 actual working. The limits to the sensitiveness of action of the 

 instrument are chiefly imposed by the diaphragm itself, which 

 must be maintained near its neutral position, because its elastic 



