372 Notices respecting Nexv Booh. 



which this rule was derived, is generally ascribed to a Mr. Holdred of 

 London, who published a tract on the subject in 1820. A similar me- 

 thod, by Mr. Horner of Bath, appeared in the Philosophical Trans- 

 actions for 1819. It is not given, however, to one individual to ac- 

 complish the work of ages. For while we do not dispute the origi- 

 nality of either of these authors, we claim the priority of the invention 

 for a Scotsman of the name of Halbert, (schoolmaster at Auchinleck,) 

 in as far as regards the solution of equations of the third degree. 

 While Mr. Bonnycastle in his elementary treatise asserted so late 

 as 1818, that the solution of the irreducible case of cubic equations, 

 except by means of a table of sines, or by infinite series, had hitherto 

 baffled the united efforts of the most celebrated mathematicians of 

 Europe j the rule for solving cubic equations of all kinds, whether 

 reducible or irreducible, had been given by Mr. Halbert as far back as 

 1789, in his treatise on Arithmetic, published at Paisley in that year. 

 The inventor, after giving his rule and a variety of examples, says, 

 ' so that I reckon this method a valuable discovery, when compared 

 with the jargon we meet with in other authors about Transmutations, 

 Limitations, and Approximations, and what brings us never the nearer 

 our purpose.' 



" 184. The step from the solution of the irreducible case of cubics 

 to that of equations of all degrees, was evidently very easy, from the 

 nature of the rule there given. Besides, it is a singular circumstance, 

 that Mr. Holdred is said to have been in possession of his method for 

 a length of time previous to publication, which tallies almost exactly 

 with the date of Mr. Halbert's treatise. — Such are the facts respecting 

 this invention, and we now leave the mathematical world to draw its 

 own conclusions, and award the honour to whosoever it is due. In 

 his next pnblication, the author may be induced to unfold this subject 

 a little more than it is possible for him to do in the present, without 

 encroaching on his prescribed limits." 



Description of Six New Species of the Genus Unio, embracing the Ana- 

 tomy of the Oviduct of one of them, together with some Anatomical 

 Observations on the Genus. By Isaac Lea. — Read before the Ame- 

 rican Philosophical Society, Nov. 2, 1827. — Extracted from the 

 Transactions of the Am. Phil. Soc. Ato, p. 15. Four coloured en- 

 gravings. 



The following are the specific characters, habitats, Sec. of the Uniones, 

 described and well-figured in this memoir. 



1. Unio Calceolus. — Testd incequilaterali, transversd, aliquan- 

 tulum cylindraced, tenuiter rugatd; dente cardinali prominente. 



Hab. Ohio. T. G. Lea. My cabinet. Cabinet of Prof. Vanuxem. 



2. Unio lanceolatus. — Testa transversim elongatd, compressa, 

 postice subangulata ; valvulis tenuibus ; umbonibus vix prominentibus ; 

 dente cardinali acuto, obliquo. 



Hab. Tar River at Tarborough. My cabinet. Professor Vanuxem's 

 cabinet. Cabinet of the Academy of Natural Sciences. Mr. Nicklin's 

 cabinet. Peale's Museum. 



3. Unio donaciformis. — Testd incequilaterali, transversd, curvaid, 



rugata ■ 



