VOL. LXXIX.] PHILOSOPHICAL TRANSACTIONS. 529 



tions, and a first, though late one, to the latter: and as fructification chiefly 

 depends on rain falling at the latter end of the season of flowering, this rain set 

 the blossoms of wheat, and of the useful fruit-trees ; as the great rains in August 

 swelled the kernel, filled, as they term it, the bushel, and gave an opportunity 

 for a 2d crop of turneps that proved more vigorous than the first. 



y. On the Method of Determining, from the Real Probabilities of Life, the 

 Value of a Contingent Reversion in which Three Lives are involved in the Sur- 

 vivorship. By Mr. JVm. Morgan, p. 40. 



In a paper which Mr. M. lately communicated to the r. s. respecting the 

 method of determining the values of reversions depending on survivorships be- 

 tween 2 persons from the real probabilities of life, he observed, that the investi- 

 gation of those cases in which 3 lives were involved in the survivorship, though 

 attended with much more difliculty, might however be effected in a similar manner. 

 The further pursuit of this subject convinced him that, as it is never safe, so it 

 can never be necessary to have recourse to the expectations of life in any case; 

 and that the solution even of those problems which include 3 lives, is far from being 

 so formidable as at first sight it appears to be. Mr. M. is sensible of the impropriety 

 of entering minutely in this place into the vast variety of propositions which 

 refer to the different orders of survivorship among 3 lives; but as the following 

 problem seemed to be of considerable importance on account of its being applied 

 to the solution of many other problems, the demonstration of it might not be 

 thought an improper addition to his former paper. The problem is this: Sup- 

 posing the ages of a, b, and c to be given; to determine, from any table of 

 observations, the value of the sum s payable on the contingency of c's surviving 

 B, provided the life of a shall be then extinct. Of this prob. Mr. M. gives a 

 long and elaborate algebraic investigation. But, for all useful purposes, it may 

 suffice to refer to Mr. Morgan's separate works, as well as to those of Dr. Price, 

 whence ample satisfaction may be obtained. 



VL Result of Calculations of the Observations made at various Places of the 

 Eclipse of the Sun, which happened June 3, 1788. By the Rev. Joseph 

 Piazzi*, C.R., Prof of Astronomy at Palermo, p. 55. 



The methods of computing the longitudes of places, from the observations of 

 solar eclipses, are well known. This M. Piazzi has here undertaken to do for 

 several different places, from which he has collected the observations made on 

 the above mentioned eclipse. . 



The observations of Loampit-Hill, Greenwich, and Oxford, as they serve for 

 the basis of all his calculations, Mr. P. has calculated them 2 different ways, viz. 

 * The celebrated discoverer of one of the lately found planets. 



VOL. XVI. 3 Y 



