18 Dr. Booth on the Rectification and 



per cent. 



Fluoride of calcium 1*86 



Soda 1-08 



Chloride of sodium 2*42 



Magnesia and chloride of magnesium . 3*50 



Twelfth. Analysis of a portion of a recent skull. 



per cent. 



Organic matter SS'iS 



Phosphate of lime 51*11 



Carbonate of lime 10*31 



Fluoride of calcium* 1*99 



Soda 1-08 



Chloride of sodium '60 



Magnesia and phosphate of magnesiaf 1*67 

 It is perhaps unnecessary to add more to these analyses 

 than the statement that they have been performed with great 

 care, and that to these and congeneric inquiries I have devoted 

 some months ; while pursued as they were in the laboratory 

 of University College, I had the advantage of most able advice 

 and assistance^. I am, &c., 



London, June 7, 1844. J. MiDDLETON. 



IV. On the Rectification and Quadrature of the Spherical 

 Ellipse. By the Rev. James Booth, LL.D., M.R.I. A., 

 Vice-Principal of, and Professor of Mathematics in Liverpool 

 College §. 



IN the livraison of the Journal de Mathematiques published 

 in September 1841, a paper is given on the quadrature 

 of the spherical ellipse, but as the method there adopted, 

 although the established one in inquiries of this nature, ap- 

 pears in the present instance somewhat complex, and as the 

 author, M. Catalan, has confined himself to merely reducing 

 the quadrature to the evaluation of a complete elliptic func- 

 Hon of the thi7-d order, without noticing or appearing to be 

 aware of the singular relation which exists between the lengths 



• So far as an inference may be drawn from qualitative indications, the 

 bone of a foetus of 6^ months contains as great a proportion of fluoride 

 as that of an adult ; an interesting fact, and not, I believe, previously no- 

 ticed. 



t If none of the magnesia existed in the bone as phosphate, which there 

 is much reason to doubt, the phosphate of lime would be increased about 

 1 per cent; the fluoride of calcium would be therefore proportionally di- 

 minished. 



I [The results of M.M. Girardin and Preisser's analyses of ancient and 

 fossil bones will be found in Phil. Mag. S. 3. vol. xxiv. p. 18.— Edit.] 



§ Communicated by the Author. 



