xv.] ANALYSIS OF QUANTITATIVE PHENOMENA. 349 



The exact definition of the standard of length is one 

 of the most important, as it is one of the most difficult 

 questions in physical science, and the different practice of 

 different nations introduces needless confusion. Were 

 all standards constructed so as to give the true length 

 at a fixed uniform temperature, for instance the freezing- 

 point, then any two standards could be compared without 

 the interference of temperature by bringing them both 

 to exactly the same fixed temperature. Unfortunately 

 the French metre was defined by a bar of platinum at 

 OC, while our yard was defined by a bronze bar at 62F. 

 It is quite impossible, then, to make a comparison of the 

 yard and metre without the introduction of a correction, 

 either for the expansion of platinum or bronze, or both. 

 Bars of metal differ too so much in their rates of ex- 

 pansion according to their molecular condition that it is 

 dangerous to infer from one bar to another. 



When we come to use instruments with great accuracy 

 there are many minute sources of error which must be 

 guarded against. If a thermometer has been graduated 

 when perpendicular, it will read somewhat differently 

 when laid flat, as the pressure of a column of mercury 

 is removed from the bulb. The reading may also be 

 somewhat altered if it has recently been raised to a 

 higher temperature than usual, if it be placed under a 

 vacuous receiver, or if the tube be unequally heated as 

 compared with the bulb. For these minute causes of 

 error we may have to introduce troublesome corrections, 

 unless we adopt the simple precaution of using the thermo- 

 meter in circumstances of position, &c., exactly similar to 

 those in which it was graduated. There is no end to 

 the number of minute corrections which may ultimately 

 be required. A large number of experiments on gases, 

 standard weights and measures, &c., depend upon the 

 height of the barometer ; but when experiments in dif- 

 ferent parts of the world are compared together we ought 

 as a further refinement to take into account the varying 

 force of gravity, which even between London and Paris 

 makes a difference of - oo8 inch of mercury. 



The measurement of quantities of heat is a matter of 

 great difficulty, because there is no known substance 

 impervious to heat, and the problem is therefore as 



