Intelligence and Miscellaneous Articles. 395 



When with these values of c the expansions of the metals by heat 

 are calculated, we obtain — 



a calculated. a observed. 



Iron 0-001070 0-001182 



Brass 0-001909 0-001878 



Platinum 0-000968 0000854 



Silver 0-001918 0-001910 



A closer correspondence was not to be expected with numbers 

 which have been determined by such different observers, and upon 

 •which certainly no shght influence is exercised by the particular 

 condition of the metals experimented with. I am at the present 

 time engaged in the determination of two of the values in question 

 — the elastic constants and the coefficients of expansion by heat for 

 the same wires — and hope then to arrive at more accurate results. 



The pressure of 224325 Russian pounds acted upon the surface 

 of TT square inches, we have then for 1 square inch 71441 pounds, 

 or more than 4327 atmospheres. 



The mechanical equivalent of heat may also be expressed in an- 

 other way. The above-mentioned metal cylinder is extended to the 



amount of h by the gravitation of one pound; the weight /j= - 



h 

 would then lengthen it one inch ; we may then express the elastic 

 force of the cylinder by saying it raises the weight p one inch ; for 

 it holds the force p which has sunk one inch in equilibrium. 



If the same cylinder is heated to 212°, it expands to the amount 

 of a ; and according to the above hypothesis, it would expand to the 

 amount of 2« if the heat acted only in one direction like the weight j9. 

 The quantity of heat which causes this expansion is w . mS, when we 

 represent by iv the quantity of heat which is necessary to raise the 

 temperature of a cylinder of water of a height and radius equal to 

 unity from 32° to 212°. Hence it follows that 

 w . otS 

 2« 

 is the quantity of heat which would effect an extension of one inch ; 

 or as forces which bring about equal effects must themselves be equal, 

 then ^ ^,,^ 



But we have also 1 , m^l 



n=- - and :=c, 



^ I 2« 



therefore w=c. 



The quantity of heat necessary to heat the cylinder of water from 

 32° to 212° is then capable of raising 224325 Russian pounds one 

 inch. Tliis cyhnder of water weighs 0-1134 of an Enghsh pound 

 (at the temperature of the greatest density) ; the number of Fahren- 

 heit degrees between the freezing and boiling-points of water is 180, 

 and a Russian pound = 0-9028 of an English pound ; wc have then 



^-0-9028 ^9901 

 0-1134.180 



