VOL. LXXXVIII.] 



PHILOSOPHICAL TRANSACTIONS. 



315 



0*20827,01655,4 X 0*43046,721 = 0*08g65,34770,9. — 4thly. Putting « + d + 

 z'V = s iv , and multiplying by a: 8 , we get z iv x 8 = 0*28046,43895.9 X 0.43046,721 

 = 0*12073,07232.90. — 5thly. Putting c -f z ir x 8 = z v , and multiplying by a? 8 , we 

 get z v x 8 = 0*38085,19524,75 X 0-43046,721 = 0*16394,42774,05. — 6thly. 

 Putting b + z v x 8 = z vi , and multiplying by x s } we get z yi x 8 = 0*60806,50444,24 

 X 0*43046,721 = 0*26l75,20631,73. 

 Lastly, to this product add a = 2*04083,30298,21, and we have the value 



of the series proposed = 2*30258,50929,94, which is true to twelve 



places of figures. 



It may not be improper to remark, that this degree of accuracy is much greater 

 than is requisite, even in astronomy ; for which, as well as for most other purposes, 

 6 or 7 places of figures are sufficient: and to that degree of exactness the value 

 of the proposed series might have been obtained, by less than a 4th part of the 

 labour that has been taken above. But it was the intention to show, that the 

 value of a very slowly converging series, of which all the terms are affirmative, may, 

 by the method now described, be computed to 10 or 12 places of figures, in the 

 space of a few hours. 



Meteorological Journal, kept at the apartments of the R. S. By order of the 



President and Council, p. 201. 



Hygrometer. 



S.SP 



90 



88 

 86 

 87 

 90 

 85 

 83 

 88 

 90 

 90 

 91 

 91 



•-5 '53 S '53 



69 

 67 

 60 

 63 

 61 

 64 

 64 

 66 

 65 

 67 

 73 

 70 



85.1 

 81.1 

 76.6 

 77.3 

 75.1 

 74.3 

 74.6 

 76.4 

 79-3 

 81.3 

 85.0 

 84 



Rain. 



Inc. 

 O..060 

 0.219 

 0.777 

 1.859 

 1.436 

 4.223 

 1.288 

 2.789 

 4.061 

 2.001 

 1.473 

 1.611 



79.2 22.697 



X. On the Stability of Ships. By Geo. Atwood, Esq. F. R. S. p. 201. 

 The stability of vessels, by which they are enabled to carry a sufficient quantity 



* The quicksilver in the basin of the barometer is 81 feet above the level of low water spring tides at 

 Somerset- house. 



S S 2 



