ELL

372

ELL

10 ) . 0040688451562500

10 ) .0004068845156250

-7.9 d

. 0000406884515625 = d

. 000366196064062511

. 0040281567046875.36

0241689402281250

120844701140625

, e

But as this rule would be much too laborious I0 ^j l0 d ?

we must content ourselves with some easy 111 gr> inapproximation : It will be very serviceable, bo .^ionSicomparing the results obtained by such appro* 1 ^y b ein order to ascertain the degree of dependence tiia jj u j e> forput on them. Let us therefore try the following o'

the periphery of the whole, the half, or the <l uathe curve. 0 f th e

Bole.— Multiply the square root of the half sU ^jjl besquares of the two axes by 3 .1416, and the produthe circumference, nearly. }ess er

Example .—Let the greater axis be 50, and theas before : the entire periphery is required

12 ) .00145013641368750012 ).000120844701140625

.00001007039176171875

11

9.11 d

E 12.12 — F

50

40

50

40

2500

1600

1600

--

. 0001107743093789062513

33232292813671875

11077430937890625

.00144006602192578125.36

2 ) 4100

20.50 ( 45.27692, the root.16

85 ).450425

00864039613I55468750432019806577734375

902). 25001804

4 ) . 00051842376789328125007 ) . 0001296059419733203125

7 ) . 0000185151345676171875

- 11.13 rf

.0000026450192239453125 = f u 14 ~ = a

Therefore, these terms collected, are as follow:

9047 ) . 6960063329

90546 ) .627100543276

905529 ) .83824008149761

a = .09b = .006075o = .00091125d = .00017940234375e = .0000406884515625f = .00001007039176171875a = .0000026450192239453125

9055382) .2326390018110764

.5153136

45.2 76923.1416

Therefore .0972190562062981640625 = the sum ofthe negative terms, which therefore being taken from 1.

.0972190562062981640625

leaves .9027809437937018359375 for the sumof the series.

Therefore . 90278 094350

45.1390 471503.1416

270 8342 8290451 3904 7151 8055 6188 604 5139 0471 5135 4171 4145

271 6 6152452 7 6921 8110 7 684 5276 9 2135.8307 6

142.2419 7 1872 ,

h g 01

The above, though agreeing only in the tw ° ^ seS infigures, is sufficiently near for most practical pu P , g 0ll lysuring; the difference in four places of fig umore than the truth.

The investigation of this rule is as follows •Let t = the greater axis,and c = the lesser,

141.8088 3052 64400 = the periphery ofthe ellipsis required.