336 



ANIMAL MECHANICS. 



from which we obtain — 



P* - p 2 = ~ 2 {a + a cos 20 J a 



+ z[d + a cos 20 } d (93) 

 + (a 2 + a' 2 + lad cos 20} 



Introducing the numerical values, I find 



14.55a' = 1 1.72a + 43-28. 



If we were to combine the four fibres in pairs, we should 

 obtain from each pair a similar relation between a and a', in 

 all of which it is easy to see that the co-efficients of a and d 

 remain the same, while the absolute term varies according to 

 the several measurements. I shall write down the results of 

 the six possible combinations : — 



Absolute Term. 



(p ~Pz) • • . 



. . . 43-28 



(p -p 2 ) . . . 



• • • 43-23 



(p -Pi) • • • 



. . . 61.65 



(Pi - p 3 ) . . . 



. > . 33.14 



(pi - P2) • . . 



. . . 25.29 



(P-2-Ps) • • . 



• • • 43- 6 3 



Mean, . . . 41 70 



The value found from the fibres p 3 ) is nearly the mean 

 value, which is what we should expect ; for the errors of 

 observation in measurement will affect equation (93) least; 

 when the differences of the fibres and the lengths of the 

 intercepts between the points of application are greatest. 

 Taking the mean value, we have 



14.55 «' = II -72 a + 41-70, 



or 



d = 0.805 a + 2.866. (94) 



