346 Mr. G. H. Knibbs : Mathematical Analysis of 



must not have E = for either £=0, or T = 0. Hence, if in 

 (17) we pnt 



*i(C) = A(l + «a;); and fc($)=B(l+£J) 



as probably sufficiently representative, we shall have, writing 

 C for AB, 



^(C)^©=C{i+«C+y3?+^C?}- • • • (i«) 



If a and ft were sufficiently small, the terms in JD? may 

 either be negligible or, within restricted limits, may be 

 compensated by adjusting the values of C, a, and ft. It 

 might therefore, with sufficient approximation, be possible 

 at least for any small range of results, to satisfy the observa- 

 tions with an equation of the form 



E=a + &T + c£ 



(19) 



or even with 



E = a' + &'Tf; ..... .(19 a) 



or yet again it may be necessary to introduce in (19) a third 

 term, viz., d . Tf. 



Solving first by the method of least squares, the whole of 

 the observations in Table I. for losses from W. A. 0. weight 

 68 kilogrammes, not affected by wind, we obtain 



E: 



33-6 + 2-93 T + 4;77f. 



This gives the values shown in column (8) of Table I. 

 These values, however, it will be seen systematically deviate 

 from the data, and show that the formula (19) cannot 

 satisfactorily represent the results. Analysing the data 

 from another point of view, we have from Tables V. and VI., 

 giving group means, the following results : — 



Table VIII. 





Obsd. 

 loss. 



Calc. 

 loss. 



Diff. 

 Obsd. -Calc. 



122-6 



60 



81 



8Ci 



95-5 

 157 

 208 

 241 



61 



72 

 93 

 104 

 150 

 203 

 245 



-1 



+ 9 



— 7 



-8-5 



+7 



4-5 



-4 



187-3 



3184 



331-8 



6630 



9806 



12336 





