560 



PHILOSOPHICAL TRANSACTIONS. 



[anno 1800. 



nearly as short a time as the inaccurate approximations which have hitherto been 

 employed for the same purpose. It may not be improper to observe, that the so- 

 lutions in these papers are not only the first which have ever been deduced, in the 

 case of 1 and 3 lives, from just principles and the real probabilities of life ; but 

 that, as to many of the problems, not even an attempt has ever been made to ap- 

 proximate to the value of the reversion. Being now possessed of correct solutions 

 of all the cases in which 2 and 3 lives are involved in the survivorship, we are 

 possessed of all that is really useful, and therefore I feel the greater satisfaction in 

 closing my inquiries on this subject. For, in regard to contingencies depending on 

 4 or more lives, the cases are not only much too numerous and intricate to admit 

 of a solution, but they occur so seldom in practice, as to render the entire investi- 

 gation of them, were it even possible, a matter of little or no importance. 



111. Abstract of a Register of the Barometer, Thermometer, and Rain, at 

 Lyndon, in Rutland, for 1798. By Thos. Barker, Esq. p. 46. 

 Barometer. Thermometer. || Rain. 



Jan. 



Feb. 



Mar 



Apr. 



May 



June 



July 



Aug. 



Sept. 



Oct. 



Nov 



Dec 



Mom. 



Aftern 



Morn. 



Aftern 



Morn. 



Aftern. 



Morn. 



Aftern. 



Morn. 



Aftern. 



Morn. 



Aftern. 



Morn. 



Aftern. 



Morn. 



Aftern. 



Morn. 



Aftern. 



Morn. 



Aftern, 



Morn. 



Aftern. 



Morn. 



Aftern. 



Highest, 



Mean of all. 



Inches. 



30.01 



30.19 



29-84 



29.88 



30.00 



29-98 



2973 



29.90 



29.77 



29.87 



29.75 



30.18 



Lowest. 



Inches. 



28.47 



28.70 



28.71 



2S.66 



28.75 



29.11 



28.91 



29.25 



28.48 



28.70 



28.21 



28.80 



Mean. 



Inches. 

 29.44 



58 

 44 

 48 

 56 

 61 

 33 

 62 

 32 

 39 

 09 

 43 



29.44 



In the House. 

 Hig. Low Mean 



461 



47 £ 



49$ 



50 



51$ 



53 



58 



61 



6i$ 



64 



68 



70 



66 



69 



66 



70 



66 



68$ 



57\ 



60 



52 



53 



42 



43 



33 



34 



35$ 



37 



40 



41* 



39 



41 



51 



51$ 



56 



57h 



57 



59$ 



60 



6lj 

 52 



51. 



44 



44 



35$ 



36 



21*. 



23$ 



40$ 

 41 



41$ 



43 



43 



44 



51 



51$ 



55 



56J 



62" 



64 



6l 



63 



63 



65 



58$ 



60$ 



52 



53 



42$ 



43$ 



36 



36$ 



51 



Abroad. 



Hig. Low Mean 







49 

 49 

 50 

 54 



48$ 



58 



52$ 



68 



62$ 



71 



69 



84 



67 



79 



64$ 



80 



62$ 



76 



55 



63 



53 



57 



42$ 



45 



28 



30 



23$ 



32$ 



28 



Z6\ 



29 

 44$ 

 44 

 52$ 

 51 

 60 

 54 

 60$ 

 51 

 62$ 

 44 

 48 

 I 32 

 43$ 

 V 



as 



15$ 

 13 



36$ 



40$ 



34$ 



43 



38 



44$ 



46 



57 



52 



61$ 



59h 

 72 



59 



70 



58$ 



70 



53 



63$ 



47 



55 



38 



43 



31$ 



35 



52 



Inch. 

 1.028 



1.542 

 0.532 

 1.321 

 1.892 

 0.950 

 2.942 

 1942 

 2.814 

 3.030 

 2.546 

 1.396 



20.938 



IV. On the Power of Penetrating into Space by Telescopes; with a Comparative 

 Determination of the Extent of that Power in Natural Vision, and in Telescopes 

 of various Sizes and Constructions ; illustrated by Select Observations. By Wm. 

 Herschel, LL. D., F. R. S. p. 4Q. 

 It will not be difficult to show that the power of penetrating into space by teles- 



