6' = l-470008-io 
rb'= 7-212704 n _ 10 
c' = 0-059041_ 10 
rc'= 5'801737_io 
Av = 8-261360_ 10 
/ 1= = 7-21412, 
a / =6'259332_ 10 
f 2 = 5-80174_ 10 
= ^ = 2-002028 
*, = 100-4681 
r = 5'742696 
fa= +0-1645 
/ 2 ^= -0-6394 
*=2 = 100°-007 C 
Interpolation by Means of a Reversed Series. 635 
quicksilver as a function of: the temperature, for tempe- 
ratures ranging from 0° to 100° C, may be written 
Av= [6-259332_ 10 ]f- [1-470008_ 10 ]* 2 + [0-059041_ 10 ]* 3 . 
Arranging the computation as before, 
AF = 
n v 
Instances may arise where it will be more convenient on 
account of the relative magnitude of the quantities to com- 
pute the coefficients of equation (2) instead of the auxiliary 
quantities/ l5 f 2 , f 3 , .... Written in this form, the inverse 
of Chappuis' equation is 
t= [3-740668] Av+ [2-692012] (Aif - [5-021349] {&v)\ (a) 
Sometimes, however, the inverted series converges so slowly 
as to be useless. Probably the best manner of handling such 
tabulated data or empirical relations is to select or compute 
n values of the function corresponding to n values of the 
independent variable and substitute in an equation of the form, 
t = A x (AiO + A 2 (At0 2 + Ao o (Avy + . . . . A„(Av)» s 
and then evaluate the n unknowns (A 1? A 2 , . . .A B ) by solving 
the n linear equations. Proceeding in this manner and using 
the values 
* = 30° C. Av= [7-736488_ 10 ] 
£ = 60° C. Av=[8-038045_ 10 ] 
£ = 90° C. Av=[8-215155_io] 
there results for the last equation, 
t= [3-740678] Av+ [2-655719] (Ar) 2 - [5-009834] (Avf. (6) 
The coefficients of (a) differ slightly from those of (£V 
Substituting At 1 = 0-0182541, the values found for t are 
; a =100°-007 C, 
and t b = 99°-999 C. 
The value £ = 100 o, 007 C. is the same as found from 
equation (3), the modified form of the general formula for 
inverse interpolation. Either of these three methods is suffi- 
ciently accurate for this problem. The last two methods are 
