576 PHILOSOPHICAL TRANSACTIONS. [aNNO 16Q3. 



same they thought it was, the stalks, leaves, and spikes agreeing exactly in every 

 thing with those of dog-mercury. He adds, it is described and figured in 

 several authors : Mr. Ray in his history of plants calls it mercurialis perennis 

 repens cynocrambe dicta, p. l63 : Gerard calls it cynocrambe, p. 333: Parkin- 

 son, mercurialis sylvestris cynocrambe dicta vulgaris, p. 295. Theatr. Botan, ; 

 Johan. Bauhine, in his second tome, lib. 23, cynocrambe mas et foemina, sive 

 mercurialis repens, p. 979: and Caspar Bauhine, in his Pinax, p. 122, mer- 

 curialis montana testiculata et spicata. 



On the proportional Heat of the Sun in all Latitudes, with the Method of col- 

 lecting the same. By E. Halley. N° 203, p. 878. 

 There having lately arisen some discourse about that part of the heat of 

 weather, simply produced by the action of the sun ; and I having affirmed, that 

 if that were considered as the only cause of the heat of the weather, I saw no 

 reason why, under the pole, the solstitial day should not be as hot as it is under 

 the equinoctial, when the sun comes vertical, or over the zenith : for this rea- 

 son, that for all the 24 hours of that day under the pole, the sun's beams are 

 inclined to the horizon in an angle of 23^ degrees ; and under the equinoctial, 

 though he come vertical, yet he shines no more than 12 hours, and is again 12 

 hours absent, and that for 3h. 8 m, of that 12 hours, he is not so much elevated 

 as under the pole ; so that he is not 9 of the whole 24 higher than it is there, 

 and is 15 hours lower. Now the simple action of the sun is, as all other im- 

 pulses or strokes, more or less forcible, according to the sine of the angel of 

 incidence, or to the perpendicular let fall on the plane ; whence the vertical 

 ray, being that of the greatest heat, being put radius the force of the sun on 

 the horizontal surface of the earth will be to that, as the sine of the sun's alti- 

 tude at any other time. These being allowed, it will then follow, that the time 

 of the continuance of the sun's shining being taken for a basis, and the sines 

 of the sun's altitudes erected upon it as perdendiculars, and a curve drawn 

 through the extremities of those perpendiculars, the area comprehended will be 

 proportional to the collection of the heat of all the beams of the sun in that 

 space of time. Hence it will follow, that under the pole, the collection of all 

 the heat of a tropical day, is proportional to a rectangle of the sine of 23°^ into 

 24 hours, or the circumference of a circle ; that is, the sine 23° 4- being nearly 

 4 tenths of radius, as-^ into 12 hours. Or the polar heat is equal to that of 

 the sun continuing 12 hours above the horizon, at 53° height, than which the 

 sun is not 5 hours more elevated under the equinoctial. 



But that this matter may be the better understood, I have exemplified it by a 

 scheme, fig. 3, pi. 14, wherein the area ZGH H is equal to the area of all the 



