230 EIGHTH REPORT — 1838. 



M/+ «V'2 = MA' 

 Eliminating o, we obtain 



2MS^(A'-/) 



CM 4- M') V'^ 

 For brevity let p = „ ^^r ^ ■ / ' H*^"*^^ 



Let 



and we have 



ti = X -pl'x (28.) 



This equation would be satisfied by/= h' ; but that would 

 involve the condition V = 0, and therefore cannot be admitted. 



The data necessary for the calculation of p will be obtained 

 by the experiments and by the levels of the line beyond the 

 foot of the gradient h'. There are also practical limits between 

 which it is certain that the mean value of / must be included. 

 Thus it is certain that f is not greater than 0*0050, and it is 

 equally certain that it is not less than 0-0015. If, then, the equa- 

 tion (28.) be tabulated between these limits, taking differences 

 sufficiently small to give the necessary approximation, the values 

 of/ may be obtained corresponding to those values of the several 

 quantities, M, M', V, &c. which are given by the experiments. 



In the case of the Whiston plane, the line rises from the foot 

 of the plane at the mean rate of 1 in 936. We shall have, there- 

 fore, the following values for the quantities on which ^j depends 

 in the first two experiments, the value of M' having been de- 

 termined by experiments made on the oscillation of the wheels; 



M=15-6 M' = 1-86 ^• = 32-16 A = -^ V' = 45-8. 



936 



The mean of the distances from the foot of the inclined plane to 

 the points where the train stopped in the first tM^o experiments 



