io8 



elegance of the conftruffion fo readily deduced from the equable de- 

 cription of areas. 



2. If SDO could be accurately computed, DCI, and therefore the 

 excentric anomaly, would be had direfily. But SO is computed from 

 taking SB— BO= DI— DT, when DCI is taken equal to SDC, and 

 hence one fource of error. Another fource of error arifes from taking 

 SD-DC, and therefore SO for the meafure of the angle SDO to 

 the radius DC 



The computed value therefore of SDO to radius CD=:SO=SB— B0= 



3 3 3 4 2 



DI— fine DI=DI_ — &c. =:'ie s , 9n — le s , otxj, 2m &c. confcquentiy 



the computed value of ACI=:ACD — DCI=»2 — es, ??i+{e s, 2m— e . 



; 4 — i 



sx, 3« — Is, m-\-e . ^-^s, 4m — Is, am — &c. this quantity is Icfs than the 



4 ^ 

 excentric anomaly by e . i,,s, 4m — .\s, 2m &c. The maximum of which 



is when jn = 60" or 120°, and therefore in the orbit of Mercury 

 is, regarding only the fourth power of the exccntricity, about 20". In 

 the orbit of Mars, and all the planets except Pallas, lefs than a fc- 

 cond. 



This fecond approximation is almoft as readily derived, as the firft, 

 confidcring how eafily the arch equal to the difference between an arch 

 and its fine may be obtained. 



The true value of DS being ufed the error of SDV arifes only from 



the error of SO. But becaufe SO=^— &c. and that the error of DI 



2-3 

 depends only on the third and higher powers of the exccntricity DI 

 itfelf depending on the firft power, it follows that the error of SO will 

 depend only on the fifth and higher powers of the exccntricity. In 

 praftice however, it is more convenient to ufe only the firft or fecond 

 approximation, and then if the exccntricity of the orbit requires it, to 

 obtain a farther correftion, by the method hereafter pointed out. 



On 



