SEA-FISHERIES LABORATORY. 



159 



Fig. 2. Graduated and ungraduated data of the example on p. 160. 



We now take some one ordinate (not a mid-ordinate) near 

 the mean, and we find the moments of inertia of the mid- 

 ordinates about this arbitrary origin. This gives us v x , the 

 first moment about the arbitrary origin. Subtracting this 

 value from, or adding it to, the value of the arbitrary origin, 

 according to its sign, we get the mean ; and dividing it by the 

 area we get fi x the first moment of the whole distribution 

 about the mean. We find that the latter is always zero, 

 but we must calculate it in order that we may find the limits 

 (h and l 2 ) of the distribution about the mean. 



The area of the whole distribution is, of course, simply 

 the sum of those of the trapezoids. 



Now if the equation to the straight line is y = — nx + a 



f: 



(nx -f- a) dx = area of the distribution. In finding the 



first moment what we do is to multiply each frequency by x so 



/l 2 

 [x (nx -\- a)] dx = first moment about the mean = 0. 

 I 



