METHODS OF INTERPOLATION. 

 Taule I. 



287 



Age. 



20 

 21 

 22 

 2:3 

 24 

 25 

 26 

 27 

 23 

 29 

 30 

 31 

 32 

 33 

 34 

 35 

 3(3 

 37 

 3- 

 39 

 40 

 41 

 42 

 43 

 44 

 45 

 46 

 47 

 48 

 49 



('0 



if>) 



.92 



. 90 

 . 9;> 

 .67 

 .82 

 .70 

 .67 

 .66 

 .67 

 .6s 

 .74 

 .80 

 AiS 

 .60 

 .81 

 .74 

 .63 

 .65 

 .82 

 .85 

 .87 

 .78 

 .84 

 .79 

 .94 

 . 8.5 

 .97 

 . 92 

 1. 03 

 .96 



1.07937 



. 973S6 

 .88650 

 . 81545 

 . 75897 

 . 71543 



. (;-:'.2(i 

 .<;6i(i5 



.(')4744 

 .64119 

 .64117 

 . 64632 

 . 65572 

 . 66852 

 . 6^397 

 .70145 

 .72039 



. 740;;8 



.76106 

 . 78219 

 . 8();!(i3 



! 84741) 

 . fiC'J'M 

 . 8'j: ',23 

 .91762 

 . 94359 

 .97168 



l.()025(; 



1. 031 i99 



(0 



Aire. 



. 71465 

 .74{i!)6 

 .76(;i5 

 .77713 

 .78100 

 . 77949 

 .77416 

 . 766'>5 

 . 75723 

 . 74779 

 . 73887 

 .73115 

 . 72520 

 .72144 

 . 72020 

 . 72173 

 .72617 

 . 73361 

 . 74408 

 . 75756 

 . 77402 

 . 793; '.9 

 . 81.561 

 . 84062 

 . 86838 

 . 89891 

 . 93224 

 . 96849 

 1. 00783 

 1.05053 



50 

 51 

 52 

 53 

 54 

 55 



5(; 



57 

 58 

 59 

 60 

 61 

 62 

 ()3, 

 64 

 65 

 66 

 67 

 68 

 69 

 70 

 71 

 72 

 73 

 74 

 '75 

 76 

 77 

 78 

 79 



(«) 



.97 

 l.Ol 

 1.06 

 1.31 

 1. 80 

 1.21 



1. 33 

 1.65 

 1.70 

 1.98 

 2.09 

 2.08 

 1.89 

 2.75 



2. .50 



3. 51 



3. 01 



4. 02 



4. 26 



3. 31 

 6.80 



5. 00 



6. 84 

 6.14 



4. 58 

 4. 50 



7. 53 

 11.31 

 11.69 

 15.88 



ii^) 



1. 07582 

 1. 12001 

 1. 17063 

 1. 22884 

 1. 29589 

 1.37314 

 1. 46206 

 1. .56419 

 1. 68121 

 1. 81487 



1. 96703 

 2. 13966 



2. 33480 



2. 55463 

 2. 80139 

 3. 07746 



3. 38.528 

 3. 72742 

 4. 106.55 

 4. 52541 

 4. 98688 



5. 49390 



6. 04955 



6. 65697 



7. 31943 



8. 04030 

 8. 82302 

 9.67116 



10. 58839 

 11.57845 



(c) 



1.09695 

 1. 14753 

 1.20:;02 

 1. 26399 

 1.33140 

 1.40629 

 1.48989 

 1. 58362 



1.68910 

 1. 80815 

 1.94283 

 2. 09546 

 2. 26857 

 2. 46499 

 2. 68782 

 2. 94044 

 3. 22655 

 3. 55016 

 3. 91561 

 4. 32758 

 4.79112 

 5.31163 

 5. 89490 

 G. 54713 

 7. 27489 

 8. 08521 

 8. 98552 

 9. 98373 

 11.08818 

 12. 30769 



« = 1.055791+.03S79144.r+.0024322S0.r2_|_ Q0Q1599072.13 

 -L .000004107808 .^^ 



This is tlie equation of tbe new series. Since the origin of coordinates 

 is at the middle point of the middle group, if we assign to x the values 

 —ii-^h+h ^^'1 ^^^ resulting values of u will be the terms belonging 

 to the ages 49, 50, 51, &c. When any five consecutive terms have been 

 computed in this way, and their four orders of ditt'erences arp. taken, 

 the rest of the series is readily constructed therefrom. The complete 

 series is given in column (b). It will be found that the sums of the terms 

 in the twelve-year groups 20-31, 32-43, &c., are identical with those iu 

 series («), and conseijuently the arithmetical means of the terms in these 

 groups are the same in the two series. 



Is^ext, let the required series be one of the fifth order. Taking six 

 groups of ten terms each, their suuis are : 



Si: 

 S^: 



:7.G1 

 :7.32 



S,= 8.95 S:,= 29.42 



84=14.02 Sg=80.27 



and using formula (D) we obtain the equation of the series — 



u = 1.0732474 + .04040701 .r+ .001909958 .^2+ .00007920042 x^ 

 +00000491GGG7a'^+.0000001071GG7ic^ 



