OUTLINES OF NATURAL PHILOSOPHY. 



b. If there are three observations,^ =r . -f- 



c. Attention must be paid to the signs of the differ* 

 ences. The succeeding quantity is here always 

 subtracted from the preceding, and therefore if 

 the former is the greater, the difference will be ne- 

 gative. On the subject of interpolation, See NEW- 

 TON, as above quoted. STIRLING on Infinite Se- 

 ries ; LA CAILLE, dstron. p. 69. $ Nautical Al- 

 manack, explanation at the end. 

 Interpolations of this kind, cannot be supposed to exr 

 tend far beyond the interval within which the ob- 

 servations are contained, unless it shall appear, on 

 continuing the observations, that the formula ap- 

 plies to them, without requiring the addition of 

 new terms. As long as the addition of new obser- 

 vations requires an alteration in the formula, it is 

 certain that the true law is not discovered. 



234. Let it now be supposed, that the form 

 of the function is known from theory, but that 

 the constant quantities which enter into that 

 function* as co-efficients of the different terms, 

 are to be found from observation ; required, 

 considering that every observation is liable to 

 error, in what way these quantities may be most 



accurately determined. 



There 



