72 PHILOSOPHICAL TRANSACTIONS. [aNNO 1791. 



but about 52 fathoms in the extent of 8° 4& 44") would be somewhat extraor- 

 dinary, were we certain that the latitude of Perpignan (42° 41' 56) is correct; 

 but this is suspected by M. de la Caille. See Mem. de I'Acad. 1758. The com- 

 puted arc however, between Greenwich and Paris, is 19 fathoms longer than the 

 measured arc, which answers to a little more than 1" of latitude. The longitude 

 of Paris on this ellipsoid is Q"* 20-^^. 



If it be contended, that the operations at the equator and polar circle were as 

 correct as those executed for the like purpose in middle latitudes; and that a kind 

 of mean between the extreme results ought to be preferred ; we shall still get an 

 ellipsoid, whose axes are nearly as 229 to 230, by taking the degrees at the equa- 

 tor and polar circle each 70 fathoms less, and that in latitude 50° 9-|-' as much 

 greater than the measured ones; and the longitude of Paris will be found 9"* 

 ]9_7_.\ But the computed meridional arc between Greenwich and Paris will ex- 

 ceed the measured one by a quantity answering to about 1 \" of latitvide. 



It is almost needless to observe, that the longitude of Paris (9'" 20^) deduced 

 by Dr. Maskelyne from the different results found by astronomical observations, 

 Phil. Trans. 1/87, agrees to less than half a second with either of the above de- 

 terminations. 



XFIL On the Method of determining, from the Real Probabilities of Life, the 

 Values of Contingent Reversions in which Three Lives are involved in the Sur- 

 vivorship. By Mr. Wm. Morgan, F. R. S. p. 246. 



Having been encouraged to the further pursuit of the doctrine of survivorships 

 by the very honourable manner, says Mr. M., in which my 2 former papers on 

 this subject were received by the r. s., I think it my duty to submit the result of 

 my labours to their consideration. The solutions of some of the following pro- 

 blems might have been derived from those which I have already communicated; 

 but the direct investigation of each separate problem being certainly more satis- 

 factory, and the rules obtained by this means in general more simple, I have con- 

 sidered no problem as connected with another, except the relation between them 

 either immediately arises from the solution, or is necessary to prove the truth of 

 it. Being anxious to render myself as concise as possible, I have been minute 

 only in the investigation of the first problem, and have done little more than 

 state the contingencies which will determine the survivorship in the others. By 

 the assistance however of these, and the operations which are detailed in my 

 former papers, the theorems which I have given may be deduced without much 

 difficulty. 



Mr. M. then gives the analytical solution of several curious cases in this sub- 

 ject; but for the practical usefulness of observations on it, it may be sufficient 

 to refer to tlie author's ingenious treatise on annuities and reversions. After 



