100 On a Proposed New Method of Weighing, 



with the temperature, or the mean expansion of the upper 

 bar of the beam may be greater than that of the under bar. 

 The variation of the sensibility of the balance is so large 

 that it is necessary to determine the weight equivalent to a 

 given number of parts of the scale for each set of observa- 

 tions, except in cases when the temperature is very nearly 

 the same." 



Between 60° and 87° Fahr. the expansion of each arm of 

 a 10 in. balance is 14 ten-thousandths of an inch; if, for 

 example, one arm of a balance were thus expanded, the 

 opposite arm remaining of its original length ; in that case, 

 as the load multiplied into the length of arm is equal to the 

 opposite load multiplied into the length of its arm, it follows 

 that ten grains on the elongated arm would balance ten 

 grains and '003 of a grain on the opposite shorter arm. But 

 although - 003 of a grain is a minute quantity regarded in 

 the individual sense of so much gold, it is far from insigni- 

 ficant regarded in relation to the ten grains representing the 

 mass assayed. Three ten-thousandths of a million sterling 

 is no less than £300, and although it is not pretended that 

 any inequality of the length of the arms at all approaching 

 this proportion could occur through inequality of tempera- 

 ture or inequality of the coefficients of expansion in the 

 mass of metal of which the beam consists, it at least shows 

 that very small differences, due either to molecular constitu- 

 tion of the material of which the beam is made, or to 

 inaccurate workmanship, can sensibly affect the results, and 

 Dr. Miller's observations teach us that differences due to 

 such causes actually exist in a measurable amount. 



The adjustment of the centre and exterior knife-edges, 

 even when the greatest care and skill are observed, is, at 

 best, no more than a very close approximation to accuracy ; 

 with this closest approach properly ensured for one tempera- 

 ture, we are not to expect that it will obtain with certainty 

 at another. If our desire is that of obtaining, under the 

 limiting conditions of rapid execution of the work, &c. 

 (which always belong to the bullion assa}-), the utmost 

 accuracy of result, in this case it would appear that our 

 attention should be devoted especially to the accuracy of the 

 weights, and to such a system of work as will adopt all the 

 reliable efficiency of the balance, at the same time counter- 

 acting the mixed and variable defects of the kind already 

 mentioned. The modes of " double weighing," those of 

 Borda and Gauss, are examples of methods by which a com- 



