32 THE VOYAGE OF H.M.S. CHALLENGER. 



It has been stated in the text that the diameters of the aneurism and of the bore appear mag- 

 nified in the same proportion. Hence it was only necessary to measure them carefully, in terms of 

 any common unit, by means of a small telescope with a micrometer eyepiece, in order to find the 

 value of n in the above expression. 



I have not thought it worth while to attempt the complex problem of calculating the effect of 

 pressure on the aneurism, having simply assumed that the volumes of all parts of the bore are 

 diminished in the same proportion, viz., by r \){)th for each ton-weight of pressure. This makes all 

 my numbers in the llth column of the table too small. But the error is of no consequence except for 

 one or two of the instruments, in which the aneurism appears almost to fill the whole external 

 diameter of the tube ; and, even then, it will in no case affect the first figure of the tabular result. 

 A somewhat greater error (also in defect) affects the numbers in the 10th column, for I have not taken 

 account of the aneurisms at the bends of the tube. These are, however, in all cases much smaller than 

 that first referred to, and the numbers for the maximum index are of no great practical importance. 



APPENDIX C. Heating of Water by Compression. 



In the paper referred to in the text, Sir William Thomson gives for the rise of temperature of a 

 fluid, the pressure on which is suddenly raised from p to^-f-w, the general expression 



ft 



Here t is the absolute temperature of the fluid ; e its coefficient of expansion, and K its average 

 capacity for heat, under constant pressure, between^) a.ndp+vr. J is Joule's equivalent. 

 The value of e, as given by Kopp's experiments, is nearly 



<-278 

 72,000 ' 



for temperatures within 20C. of the maximum density point. The mean of the experimental deter- 

 minations of Matthiessen, Pierre, and Hagen, makes it about 5 or 6 per cent, greater. 



For the Centigrade scale the value of J is 1390 foot-lbs. An atmosphere of pressure is nearly 

 2117 Ibs. weight per square foot ; and K is about 63'45 (the number of pounds of water in a ciibic 

 foot). 



Hence it follows that, for one additional atmosphere of pressure, the temperature of water is 

 raised (in degrees Centigrade) by about 



2,850,000 ' 



Now 56 F. is 133 C., for which = 287'3, and the rise of temperature produced by a ton- weight per 

 square inch is 



0-14 C. or 0-25 F. 

 This is the statement in the text. 



