MEASUREMENT OF ANGLES. 



If we assume that the value of the divisions of the scale at a 

 temperature / , but little different from ordinary temperatures, is e , 

 we shall have 



and therefore 



The value* of the coefficient A, vary from 8. io~ 6 to 2o.io~ 6 for 

 ordinary metals; a change of temperature of 10, would at most 

 necessitate a correction of 2 in ten thousand, which in most cases 

 could be oeg/ected. 



If the object to be measured is itself at the temperature /, and 

 we desire to know its length 7 at zero, then if A is the coefficient 

 of expansion, 



i + A'/' 



This second correction is of the same order of importance as 

 the first. 



657. The balance enables us to ascertain the equality of two 

 apparent weights. If P is the true weight of the body weighed, 

 TT the actual weights which balance it, D, A, and 8 the specific 

 gravities of the body, of the weights, and of air, we have 



from which, with sufficient approximation, 



In order to give an idea of the importance of this correction, the 



rt j> 



values of D, of and of the expression for a few bodies, 



