370 THE SCIENTIFIC PAPERS OF 



bottom, connected by a tube of such diameter that its area, 

 compared with that of the cups, might be neglected in calculation, 

 it is evident that the potential of such a column would vary with 

 the temperature in the ratio of the dilatation of mercury ; in other 

 words, the absolute height of the column would remain practically 

 the same at all temperatures, whereas the density of the mercury 

 would vary in the well-known ratio of '00018153 per degree C. 

 If a spring could be found whose ratio of variation was less than 

 that required for the mercury, it is evident that between these 

 extreme forms one might be found in which the two ratios of 

 variation would be exactly alike. The ratio of variation of the 

 steel springs depend upon their degree of hardness ; and in the 

 case of the instrument here referred to it amounted to '000258, or 

 was in excess of the compensating power furnished by the mercury. 

 Complete compensation could therefore in this case not be ob- 

 tained, although the remaining error is extremely small, and was 

 rendered practically inappreciable by allowing the comparatively 

 inelastic diaphragm to take a portion of the mercurial pressure. 



The proportion, as resulting from calculation, would at any 

 rate have to be modified in order to allow for the linear expansion 

 of the steel composing the tube as affecting its capacity ; but this 

 expansion proceeding also in an arithmetical ratio will only affect 

 to a small extent the precise relative diameter to be given to the 

 tube, without in any way disturbing the ratios of arithmetical 

 increase upon which the compensation of the instrument is based. 

 An easy verification of this arrangement, which may be called a 

 parathermal system of adjustment between gravitation and elastic 

 force, is furnished in suspending the complete instrument in the 

 hot-air chamber in which the experiments for variation of elasticity 

 were made, when the variations of temperature gradually and 

 artificially produced within the chamber should remain without 

 effect upon its reading. 



On subjecting the first instrument constructed on this principle 

 to this test, a variation was discovered amounting to '00000125 

 per degree C., which was not corrected, however, in trying the 

 instrument on board the steam-ship " Faraday ; " and the results 

 then obtained, and given below, have had to be adjusted to this 

 extent for variation in temperature. 



INFLUENCE OF VARIATION IN ATMOSPHERIC DENSITY. The 



