478 KEPORT — 1882. 



The cup (E) must be so shaped that the end of the caplllaiy tube (D) never 

 emerges from the surface of the mercury in the cup, and that this may be the case the 

 descent of the cup due to the introduction of a given quantity of mercury should 

 not be greater than the height which the mercury introduced occupies in the cup ; 

 or, in symbols, if o- is the area of the cup, I the unstretched length of the spiral 

 spring, and a the volume of mercury required at (D) to stretch it to double its natiu-al 

 length, 



then o- = 77 <^-y 



It will be seen that, by taking a properly proportioned spring and cup, the 

 thermometer may be made to record to any desired scale ; but the limit to the 

 accuracy of the record is of course fixed (for any given thermometer) by the 

 constant fi-iction of the moving parts. This, however, can without trouble be made 

 very small. 



To apply the mechanical method to the barometer it is only necessary to hang 

 the barometer tube to the lever (F) instead of the cup (E), allowing the open end 

 to dip into a deep fixed cistern. 



The greatest part of the weight of the merciu-y in the tube should of course be 

 counterbalanced, leaving only the variable part to be taken by the spring. The 

 variation of the barometer alters the extension of the spring by a quantity directly 

 proportional to the variation of the weight of the column of mercury supported ; 

 thus the curve drawn by this Idnd of self-recording barometer requires no correc- 

 tion for temperature, except a small term depending on the expansion of the glass. 

 The rise or fall of the tube in the mercury cistern gives rise to a force depending 

 on tlie flotation of the immersed part of the glass tube ; but as this force is a linear 

 function of the rise or fall, it makes no difference in the character of the curve 

 traced Ijy the instrument, and is equivalent merely to an alteration of the value of 

 (a) which measures the stifthess of the spring. 



7. On a Musical Instrument. IDij J. Philips. 



8. On an Arithmetical Model. Bij Sir F. J. Bramwell, F.B.S. 



