150 Maine Agricultural Experiment Station. 1917. 



The observed curve shows itself at once to have the general 

 shape of a logarithmic curve and not a straight line, as has been 

 the general opinion of dairymen as stated earlier.^ In grad- 

 uating this curve the points determined by the coordinates of 

 the first array and the arrays beyond the one whose mid-point 

 is 16 years 9 months should be disregarded because of the 

 paucity of observations in the original table. For the same rea- 

 son too much weight should not be put on any of the points 

 above 12 years 3 months. The first part of the observed curve, 

 where the frequency of observations is large, is quite smooth 

 and shows well the general type of curve which will best fit. 



As a first approximation a curve of the form 

 y — a-\-bx-\-cx^-\-d log x 

 where y^production and .i'=age was fitted by the observations. 

 The value of the constants a, b, c, and d were determined by the 

 method of least squares. This curve closely fitted the data at 

 the points near the middle of the range, but it failed at the ends. 

 The nature of the discrepancies was such as to indicate that 

 better results would be got by a slight modification of this same 

 general type of curve. This proved to be the case. The final 

 curve, from which the smooth curve of Figure 7 is drawn is 



y=188.0224— .0707 ^-^+69.8997 log x 

 This curve obviously gives a practically perfect fit. 



In Table 2 are given the theoretical average seven-day milk 

 production as calculated from this curve for each month in age 

 from 1 year 9 months to 16 years 9 months. 



^The fact that milk production age curves were generally of logarithmic 

 form was first announced in a preliminary paper by Pearl (Proc. Soc. 

 Exp. Biol, and Med. Vol. xii, pp. 18-19, 1914.) several years ago. The 

 present paper furnishes the first detailed exhibition of the evidence on 

 which the preliminary announcement was based. It was hoped that a series 

 of several papers would immediately follow this one on the Jersey seven- 

 daj' records, in which a large mass of evidence from the records of pro- 

 duction of other breeds would have been presented. This has been ren- 

 dered impracticable for the present by the fact that the senior author has 

 been called to wholly other lines of endeavor for the duration of the war. 

 In the meantime attention should be called to the fact that the Holstein- 

 Friesian 7-day fat production curve worked out in this laboratory has 

 been published, but without discussion, (cf. Miner, J. R. Jour. Agr. Re- 

 search, Vol. 3, pp. 417-420, 1915.). 



