VOL. LXXXVIII.] PHILOSOPHICAL TRANSACTIONS. 341 



There was a remarkable circumstance attending this case, which ought not to be 

 lost sight of, viz. the extraordinary quantity of liquor amnii, which had been con- 

 tained in the ovum. What connection there was between this and the tumour, 

 cannot be absolutely explained from a single instance, as there did not seem to be 

 any direct communication between the tumour and the cavity of the amnion. The 

 whole of it lay, as has been before related, behind the chorion ; so that between it 

 and the cavity of the ovum there were 2 membranes interposed. In its organi- 

 zation, it had all the appearance of a glandular part, and was extremely vascular; 

 but no duct could be found leading from it into the cavity of the ovum. Yet, 

 though it may appear difficult to prove, that the quantity of liquor amnii depended 

 on this substance, still, as it so considerably exceeded that which is found in com- 

 mon, or has ever been described, it is reasonably to be believed that it did so. The 

 manner however by which the secreted fluid was conveyed from the tumour into 

 the general cavity of the ovum, must still remain unaccounted for. 



XVI. Qn the Roots of Equations. By James Woody B. D. p. 369. 



The great improvements in algebra, which modern writers have made, are chiefly 

 to be ascribed to Vieta's discovery, that " every equation may have as many roots 

 as it has dimensions." This principle was at first considered as extending only to 

 positive roots; and even when it was found that the number might, in some cases, 

 be made up by negative values of the unknown quantity, these were rejected as 

 useless. It could not however long escape the penetration of the early writers on 

 this subject, that in many equations, neither positive nor negative values could be 

 discovered, which, when substituted for the unknown quantity, would cause the 

 whole to vanish, or answer the condition of the question ; in such cases, the roots 

 were said to be impossible, without much attention to their nature, or inquiry 

 whether they admit of any algebraical representation or not. As far as the actual 

 solution of equations was carried, viz. in cubics and biquadratics, the imaginary 

 roots were found to be of this form, (a -f 4/ — Z> 2 ); and subsequent writers, from 

 this imperfect induction, concluded in general, that every equation has as many 

 roots, of the form (a ± */ ±b 2 ), as it has dimensions. In the present state of the 

 science, this proposition is of considerable importance, and its truth ought to be 

 established on surer grounds. The various transformations of equations, the dimen- 

 sions to which they rise in their reduction, and the circumstances which attend their 

 actual solution, are most easily explained, and most clearly understood by the help 

 of this principle. Mr. Euler appears to have been the first writer who undertook 

 to give a general proof of the proposition; but whatever may be thought of his 

 reasoning in other respects, as he carries it no farther than to an equation of 4 

 dimensions, and it does not appear capable of being easily applied in other cases 



and it directly interferes with the offices of the placenta, which no longer performs perfectly the func- 

 tions for which it was designed. Nourishment and vital air are no longer supplied properly to the fcfctus, 

 which therefore commonly dies.— Orig. 



