OF ARTS AND SCIENCES. 27 



Writing for brevity, 



,. , ^- ^ K, a constant; 



2h' — 1h- 

 Pi—P-2 



(f) (p), a function of p ; 



and 



there results, 



~^ ' • = ■vl/- (t), a function of t ; 



y = K . <t>(p) . ir(t). 



Differentiating this expression successively with respect to K, p^, p^, 

 jo.j, t, A, and a, then substituting for c?y, dK, dp^, &c. A//, AK^Ap^, &c., 

 and solving with respect to A A", Ap^, &c., the following expressions 

 may be obtained: 



^.- (Plj^ini L_ .A, 



(Pi^ — Po^y 1 



?),- — p«- 1 



a K . (p {p) 



I 4-at 1 



aA= ■ ■ • • A V 



3t K.fpip) -^ 



^° — {i-{.-SAt)t ' K . ({> {p) ' ^" 



From these, by inserting the proper numerical quantities taken from 

 any suitable experimental result, may be computed the numerical 

 values of A A', A/>,, &c., corresponding to any assumed value of Ay, and 

 thus may of course be found the amount of change (or error) in K, 

 jtJj, &c., which would produce in y the assumed change (or error) A y. 



For the present purposes it is convenient to assume for Ay the same 

 fractional value at all temperatures, and a convenient and suitable 

 magnitude is Ay = 0.001 y. The following Table VIII. gives the 



