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THE AMERICAN NATURALIST [Vol. XLV 



3. The use of the tables may be illustrated from a concrete ex- 

 ample based on data collected in this laboratory. Each of the 

 successively laid eggs of a certain hen were measured, length 

 and breadth being recorded. From these records the length- 

 breadth index (100 breadth -f- length) was calculated. In all 87 

 eggs were measured. 6 To the line given by plotting the value of 

 the index of each of these eggs in consecutive order as they were 

 laid a curve of the type 



y = a + bx + c(log x) 

 was fitted by the method of least squares. In this equation y de- 

 notes the value of the length-breadth index of an egg whose 

 ordinal number in the whole series laid is x. That is, S(x) will 

 be the sum of the integers from 1 to 87 inclusive. 



The type equations for this curve have been given above 

 (p. 756) and need not be repeated. For the data under discus- 

 sion n = 87. From the table given in the present paper we 

 read off at once 



8 log x = 132.3238, 

 S(x log x) =6,602.9556, 

 S(logx) 2 = 215.0293. 

 Further from Elderton's table (loc. cit.) we get 



S( x*) =223,300. 

 This leaves to be obtained by actual addition from the data 



S(y) =5,473.81, 

 S(xy) =245,041.55, 

 S(y log x) =8,416.4497. 

 Substituting these values in the type equation (iii) we have 

 87a + 3,8286 + 132.3238c = 5,473.81, 

 3,828a + 223,3005 + 6,602.9556c = 245,041.55, 

 132.3238a + 6,602.95566 + 215.0293c = 8,416.4497. 

 Solving 



y = 49.0241 — .0910* + 11.7669 log *. 

 The goodness of fit of this curve may be judged by examination 

 of Plate II of the paper where the original data are published. 7 



of Experimental Zoology, VI, 349. 

 % Jour. Exper. Zool., loc. cit. 



