VOL. L.] PHILOSOPHICAL TRANSACTIONS; 307 



of the radius, as ab x p^ to 4tp. Therefore, if p denote the 4th part of the 

 planet's periodic time about the earth, the total acceleration of the earth's mo- 

 tion about its axis, generated in the passage of the planet from the equinox to 



the solstice, will be = — ; and the retardation will be the same in the 



planet's transit from the solstice to the equinox. Hence naturally arises this 

 theorem : " The square of the diameter is to the square of the sine of ecliptic's 

 obliquity, as the 4th part of the periodic time of the sun or moon, is to another 

 time; then the earth's semidiameter is to the difference of the semiaxis, as the 

 time just found, is to the acceleration sought. 



The rise ab of the water due to the sun's force is about 2 feet, the earth's mean 

 semidiameter tp being 1 96 15 800; hence the theorem produces, for the earth's 

 acceleration turning about its centre, made while the sun passes from the equinox 

 to the solstice, the quantity 1"' 55"' in parts of time. And if by the moon's 

 force the waters rise to the height of 8 feet, the acceleration of the earth's rota- 

 tion hence arising, while the moon moves from the equator to her greatest de- 

 clination, will be 34"". And the sum of these accelerations, which obtains 

 when these two planets occupy the solstitial points, since it exceeds not 2\'" of 

 time, or 3"]'" of a degree, will hardly be sensible, a. e. i. 



CXI. Observations on the History of the Norfolk Boy. By J. Wall, M.D. p. 836. 



Dr. W. attributes the evacuation of worms in this boy's case to the oil in the 

 mixture of paint which he swallowed ; and mentions that he had afterwards pre- 

 scribed oil as a vermifuge, with good success. 



CXII. On the Corona Solis Marina Americana ;* l^he American Sea-Sun-Crown. 

 From the French of J. A. Peyssonel, M. Z)., F. R. S. p. 843. 



CXIIT. On several Rare Species of Barnacles. By J. Ellis, Esq. F.R.S. p. 845. 

 Some rare and extraordinary new species of barnacles, lately received from 

 abroad, were so different from any of the common species, that Mr. E. was re- 

 solved to inquire into the nature of an animal, which, like a Proteus, appears in 

 so many different shapes or coverings in different parts of the world. For this 

 end he consulted that excellent collection in the British Museum, and some others 

 in the cabinets of his friends. This marine animal is called by writers on natural 

 history, balanus, and concha anatifera: but Linneus calls the internal active part, 

 or fish, the animal triton, and the covering or testaceous habitation lepas, which 

 he says is a multivalved shell, composed of unequal valves. The animal triton 

 he describes, as having an oblong body, a mouth with a tongue in it, twisted 



* This is some species of actinia, but for want of a figure, it is hardly possible to tell what parti- 

 cular species is intended ; neither is the description clear, so that it was thought not worth reprinting. 



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