VOL. XLir.] PHILOSOPHICAL TRANSACTIONS. 713 



from the greatest knowledge in geometry. How they arrive at this, and how the 

 wonderful instinct in animals is to be accounted for, is a question of a higher 

 nature ; but this is surely a remarkable example of this instinct, as it has sug- 

 gested a problem that had been overlooked by mathematicians, though they 

 have treated largely on the maxima and minima ; and such a one, as has been 

 tiionght to exceed the compass of the common geometry. 



It may be worth while to add here, that if the cells had been of any other 

 form than hexagonal, and the bases had still been pyramidal, these must have 

 been terminated by trapezia, and not by rhombuses, and therefore had been less 

 regular, because oa and ak would have been unequal : nor could there iiave 

 been room for such an advantageous or frugal a construction as that we have 

 described, because the solid content of the cell would have increased with the 

 right line ke. The cells, by being hexagonal, are the most capacious, in pro- 

 portion to their surface, of any regular figures that leave no interstices between 

 them, and at the same time admit of the most perfect bases. Thus, by follow- 

 ing what is best in one respect, unforeseen advantages are often obtained ; and 

 what is most beautiful and regular, is also found to be most useful and ex- 

 cellent. 



On the Transit of Mercury over the Sun, April 17, 1740 ; and of an Eclipse of 

 the Moon, Dec. 21, 1740. By Mr. John fVinthrop, Hollisian Professor 

 of Mathematics and Astronomy at Cambridge in New England. N°471, 

 p. 572. 



Mr. W. being advertised, by the calculations of Dr. Halley, that the former 

 part of this transit would be visible in his horizon, was resolved to observe 

 it in the best manner he could, with the few instruments he was furnished with. 

 He expected that the centre of the planet would enter on the sun at 5** 2"" ; but 

 being apprehensive that he might be earlier than the calculation, he for some 

 time before that, with a 24-foot tube directed to the sun, kept his eye fixed on 

 that part of his limb where the planet was to enter, as steadily as he could for 

 the wind, which then blew fresh. This precaution was not needless ; for at 

 4*^ 54^" 59% he perceived that Mercury had made an impression on the sun's 

 limb ; by the quantity of which he concluded, that almost one quarter of his 

 diameter might be entered. Hence he continued to watch the planet's pro- 

 gress ; but unfortunately, by a shaking of the tube, he missed the moment of 

 is interior contact with the sun's limb, but was certain it could be but very 

 little later than 5*' 0"" 40*; for he presently after saw him fairly within the sun. 

 From several observations made during the transit, Mr. W. infers, that 

 Mercury's horary motion in longitude from the sun, was now 3' 58'; accord- 

 voL. vm. 4 Y 



