268 



CATALOGUE OF POLAK STABS. 



REDUCTIONS FROM 1875 TO 1955. 



h. m. s. 

 1875.0 Ofl = 7 29 5.G310 



lAtnitations in the Method of Development hy Differential Coefficients. 



That the method of development by means of differential coefficients expres.sed 

 in terms of the ascending powers of the time has certain limitations in its ap- 

 plication will be evident from an examination of the residuals Y^ — F4 given on 

 pages 267 and 2G8. 



The extent of this limitation may be shown in the following manner. Let 

 us assume that an error x occurs in the initial function where its effect will 

 be a maximum. The magnitude of the errors in the successive orders of dif- 

 ferences will be represented by the coefficients of x given in the following 

 scheme : — 



