4i8 



Journal of Agricultural Research 



Vol. Ill, No. 5 



The calculations to obtain the moments are given in Table II. 

 Table II. — Calculation of moments for data on Holstein-Friesian cows in original form 



Age. 



1 yr. 6 mo. to I yr. 1 1 mo . . 



2 yr. to 2 yr. 5 mo 



3 yr. 6 mo. tojyr. 11 mo. - 

 3 yr.t0 3yr. s mo 



3 yr. 6 mo. to 3 yr. 11 mo. . 



4 yr. to 4 yr. s mo 



4yr. 6 mo. t0 4yr. ixmo. . 



syr. to 5 yr. 5 mo 



syr. 6rao. t0 5 yr. 11 mo. . 



6 yr. to 6 yr. s mo 



6yr. 6 mo. tobyr. 11 mo. 



7 yr. to 7 yr. s mo 



7 yr.6 mo. to 7 yr. ji mo 



8 yr. to 8 yr. 5 mo 



8 yr. 6 mo. to 8 yr. 11 mo . 



9yT. togyr. 5 mo 



9yr. 6mo. t09yr. 11 mo, , 

 10 yr. to 10 yr. s mo 



10 yr. 6 mo. to 10 yr. 1 1 mo 



11 yr. to II yr. s mo 



iiyr.6mo.toiiyr.iimo 



la yr. to 12 yr. s mo 



1 a yr. 6 mo. to 1 2 yr. 11 mo 

 13 yr. to 13 yr. 5 mo 



13 yr. 6 mo. to 13 yr. 11 mo 



14 yr. to 14 yr. 5 mo 



290. 6 

 3'6-7 

 347.0 

 376.0 

 407.9 

 428.2 

 447. I 

 457-2 

 464.2 

 466.3 

 468.0 

 466.6 

 466.6 

 467.0 

 466.6 

 464. 6 

 462.5 

 460. 7 

 460. 2 

 455-2 

 453-7 

 449.1 

 444.0 

 443-2 

 448.7 

 440.0 



Total iii3is- 45261 



326. 06732 



240.32913 



401. 76094 



361.44305 



407.9 



428.2 



447.1 



457-2 



464.2 



466.3 



468.0 



466.6 



466.6 



467-0 



466.6 



464.6 



462. s 



460.7 



460- 2 



455-2 



453-7 



449.1 



426.81041 



513. 14250 



340. 49788 



493- 70138 



326.06732 

 480. 65826 



1,205. 28282 



1,445- 77220 



2.039. 5 



2,569. 2 



3.129-7 



3,657-6 



4.177-8 



4,663.0 



5,148.0 



5,599- 2 



6,065-8 



6, 538- o 



6| 999. o 



7.433-6 



7,862.5 



8,292.6 



8,743-8 



9, 104- o 



9. 527- 7 



9, 880. 2 



9,816.63943 

 12,315.42000 



8,512. 44700 

 12,836.23588 



326. 



961. 



3.61s. 



5.783. 



10.197. 



15.415- 



21,907. 



29, 260. 



37,600. 



46, 630. 



56,628. 



67.190. 



78.855- 



91.532- 

 104.985. 

 118.937- 

 133.662. 

 149, 266. 

 166, 132. 

 182,080. 

 200,081. 

 217.364- 

 225,782. 

 295,570- 

 212,8ll- 

 333. 742- 



06732 

 31652 

 84846 

 08880 

 5 



70689 

 08000 

 17500 

 13288 



23 



SO 



92 



153- 



234' 



338. 



466. 



622 



806, 



1,025, 



1,281, 



J. 574 



1,903, 



2,272 



2,686, 



3,156 



3,641. 



4,201 



4,782 



5,193 



7,093 



5. 320 



8,677 



326.06732 



922.63304 



847- 54538 



132-35520 



987.5 



491-2 



3SS-3 



086.4 



401. 8 



300. o 



908.0 



284.8 



120. 2 

 448.0 

 775-0 



001- 6 

 262. 5 

 802.4 

 511.8 

 600. o 

 715-7 

 016.8 

 002. 25847 

 681. 92000 

 279- 37SOO 

 295. 45488 



158.369. 72291 



2.806,320.01587 



55.610.556. 60939 



For reasons which need not be considered here it is usually desirable 

 to use corrected rather than raw values of the moments. Here we have 

 used one of Elderton's (7) correction methods. The column headed y' 

 is obtained from the y column by Elderton's formula V' — i. e., by mul- 

 tiplying the first and last ordinates by 1. 1220486, the second and last but 

 one by 0.7588542, the third and last but two by 1.1578125, and the 

 fourth and last but three by 0.9612847. 



From this table we have at once M, = 1 1,315.45261 ; Mi= 158,369.72291 ; 

 Mj = 2,806,320.01 587; .1/3=55,610,556.60929; /=26. 



Substituting these values in the equations xxi to xxiv for the curve 

 y = a + bx + cx^ + d log x, the following values for the constants are found: 



d= 0.060096940 (20M3— 810M2 + 8907M,— 2i829.5A/o) = 259.833i7. 



= 0.000025250 (6M2— i62yVf, + 755.5Mo) + o.oo24io2d= —0.0533. 



& = 0.000341 37 (2Mj— 27M„) — 27c — 0.044239^= —6.225. 



a=o.03846i5M„- 13.56- 238.583333c- 1.022111^=266.38. 



The final equation then becomes 



y= 266.38- 6.225.1;- 0.0533.1-= + 259.833 logioX. 



The ordinates calculated from this equation in comparison with the 

 observations are given in Table IV. 



Before proceeding to any discussion of the fit, let us consider a second 

 example, where the ordinates are at irregular intervals. The data here 

 taken for illustration are the same as those of the preceding example, 

 except that certain of the observations have been arbitrarily combined 

 and the new values so obtained taken as ordinates. Table III shows 



'It is to be noted that the coefficieats as given by Elderton (7, p. 27) are incorrect in the last figtire. 



