VOL. XVII.] 



PHILOSOPHICAL TRANSACTIONS. 



579 



day ; for if the aforesaid sum of the sines of the meridian altitudes be multi- 

 plied by half the sum of the sines of the sun's horary distance from noon, when 

 the times are before and after noon ; or by half their difference, when both are 

 on the same side of the meridian ; and thereto in summer, or therefrom in 

 winter, be added or subtracted the product of half the arch answerable to the 

 proposed interval of time, into the difFerence of the sines of meridian altitudes> 

 the sum in one case, and difference in the other, will be proportional to the 

 whole action of the sun during that space of time. 



I foresee it may be objected, that I take the radius of the circle on which I 

 erect the perpendiculars always the same, whereas the parallels of declination are 

 unequal ; but to this I answer, that our said circular bases ought not to be 

 analogous to the parallels, but to the times of revolution, which are equal in 

 all of them. 



It may perhaps be useful to give an example of the computation of this rule, 

 which may seem difficult to some. Let the solstitial heat, in 25 and Vf, be re- 

 quired at London, lat51°32'. 



38° 28' Co-lat. Ascen.diff^. 33° ] l' 



23 30 Decl. Estival semidium. arch. . 123 11 



Sine = ,882674 Hybernal semidiur. arch 56 49 Sin. ,638923 

 Measure of the estival arch 2,14 995 5 

 Do. of the hybernal arch 991683 



61 



14 



58 



58 Sine = ,258257 

 Sum 1,140931 

 Diff". ,624417 



Then 1,140931 X ,836923 +,624417 X 2,149955 = 2,29734 

 And 1,140931 X ,836929— ,624417 X ,991638=0,33895 

 So that 2,29734 will be as the tropical summer's days heat, and 0,33895 as 

 the action of the sun in the day of the winter solstice. 



After this manner I computed the following table for every J 0th degree of 

 latitude, to the equinoctial and tropical sun, by which an estimate may be made 

 of the intermediate degrees. 



Sun ill s Sun in Vf 



18341 18341 



. 20290 15834 



. 21737 13166 



. 22651 10124 



. 23048 6944 



, 22991 3798 



22773 1075 



23543 .... 000 



24673 .... 000 



25055 ... 000 

 4 E 2 



