KXAMI'LKS XXV 



Thus giving a relation from which the value of n can be calcu- 

 latrd, and knowing n, a and b can be found. 



A fully worked out example for this curve will be found in 

 paragraph 221. 



EXAMPLES XXV 



(1) There are errors of observation in the following values of 

 y and x : 



It is found that the following two empirical formulae seem to be 

 nearly equally good : 



Find the best values of a and b, a and [3. (B. of E., 1906.) 

 (2) The following numbers are authentic ; t seconds is the record 

 time of a trotting (in harness) race of m miles : 



It is found that there is approximately a law t = a m b , where a 

 and b are constants. Test if this is so, and find the most probable 



in. 



values of a and b. The average speed in a race is s = ; express s 



p 



in terms of m. (B. of E., 1907.) 



(3) The following quantities measured in a laboratory are 

 thought to follow the law y = ab~ x . Try if this is so, and if so, 

 find the most probable values of a and b. (B. of E., 1908.) 



(4) The equilibrium position for a certain governor is that a 

 ball should be at a certain position r from an axis about which it 



/200 + 80 h\ 

 revolves, when the centrifugal force is equal to H ) where 



h = V2-25 r 2 . Now a certain mathematical investigation be- 

 comes too complex if this law is used, whereas it is known that, 

 if the centrifugal force were equal to br - a where a and b are mere 



