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LX. Memoir on a nctv mid certain Method of ascertaining the 

 Figure of the Earth by means of Occidtations of thejixed 

 Stars. By A. Cagnoli. JVith Notes and a??, appendix by 

 Francis Baily*. 



advertisement. 



The following memoir originally appeared in the Transactions of the Italian 

 Society (Memorie di Matematicn e di Fisica delta Societa Jtaliana, Tom. vi. 

 Verona 1792) : but, although it has been so many years before tlie public, 

 I do not tind that the subject of it has been taken up by any persons either 

 here, or on the continent. In fact, I believe that it is not generally known 

 in this country : and it is with a view of drawing the attention of astrono- 

 mers more closely to it, that I now present them with this translation. 

 The acknowledged talents and abilities of the author nnist at all times en- 

 sure it an attentive perusal : but particularly at this period, when a more 

 than ordinary degree of interest is excited towards the subject of the true 

 figure of the earth. I am aware that there are some apparent difficulties 

 in the method pointed out in the memoir, yet 1 am not without hope and 

 expectation that they may be eventually oveicome: and that the mode 

 herein proposed may at least be brought in aid of the other methods at 

 present adopted for determining tliat difficult problem. 



To the memoir itself I have subjoined some notes connected with the sub- 

 ject ; which, however, may be distinguished from those of the author by 

 the addition of the letter B. And to the whole I have added an Appendix, 

 wherein I have attempted to illustrate the views of the author; and ven- 

 tured to propose such methods as may best tend to carry his object into 

 execution. 

 Gray's Inn, May 20, 1819. Francis Bailv. 



Memoir, &c. 



§ 1 . J. H E truth of the Newtonian theory of universal gravita- 

 tion is proved by the wonderful agreement in all the celestial 

 phsenomena, which have hitherto been submitted to the tests of 

 calculation and of observation. There probably is not any astro- 

 nomer of the present day who is not convinced that our planet is 

 compressed, or flattened, at the poles, and protuberant at the 

 equator. In fact, if we combine this theory of Newton with the 

 hypothesis of the elliptical form of the earth, we shall find that 

 the precession of the equinoxes and the nutation of the earth's 

 axis are sufficiently accounted for. Other arguments indeed, in 

 favour of the elliptical form, may be derived from the rotation of 

 the earth, which is now generally admitted: and others again 

 from the differences in the length of the ))endulum vibrating se- 

 conds in different latitudes. Still, however, we want some theory 

 of the internal density of ihe earth ; which, it is feared, will ever 

 remain hid from human investigation. But if, to the want of 



* The present memoir has been already printed, but not for sale. It is 

 now reprinted with the polite permission of the author. 



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