VOL. XVII.] PHILOSOPHICAL TRANSACTIONS. 481 



is, as c to c — d, so is CP : CY; or, which comes to the same thing, as c 

 to d, so CP to PY : then the plane YZ parallel to the base, will cut off, from 

 the curve surface, a portion adjacent to the pole, equal to the triangle ADC. 

 And since the same holds in the other quadrants, therefore the whole surface 

 round about the pole, so cut off, will be equal to the whole square inscribed in 

 the base ; which was to be done. 



Or shorter, thus. The curve surface of the hemisphere, because equal to 

 two of its great circles, is = cr ; and the square inscribed in a great circle 

 = 2rr = <ir; and the former to the latter as c to d. Therefore (because the 

 segments of the surface cut off by parallel planes, are proportional to the seg- 

 ments of the axis) taking CP to PY as c to d, then the whole surface being 

 cr, the portion next the pole, cut off by the plane YZ, will be equal to dr, the 

 square inscribed in the base. 



Dr. Wallis adds also some other methods of performing the same thing. 



Abstract of two Letters, sent some Time since by Mr. Anth. Fan. Leuwenhoech, 

 to Dr. Gale and Dr. Hook. N° I96, p. 593. 



Having examined the testicles of a rat, and the liquor pressed out of their 

 seminal vessels, I found a great number of animalcules, long and serpent-like. 

 The liquor itself in which they floated was transparent and oily, full of irregular 

 parts, besides the animalcules, which I conceived were the rudiments of those 

 animalcules which were generated in the thread-like vessels of the testicles. 

 I suppose the manner of their generation differs from that of the eels I have 

 formerly observed in vinegar, which carry their young in their body, whereas I 

 believe these are produced from an egg. And possibly they may have their be- 

 ginning with the generation of the animal, and come to perfection together 

 with it, remaining in the seed in the testicles in fieri, till the animal itself is 

 fit for copulation; as in man till about 14 years, and then first have life and 

 perfection. 



The particular coat of these thread-like vessels is exceedingly thin ; and the 

 contained animalcules so very minute, that 10,00O of them equal not one thread ; 

 whence may be computed the vast number one testicle is capable of containing. 

 These threads are more conspicuous in the testicle of a rat than any other animal. 



Endeavouring to examine the seed of muscles in March, when they spawn, 

 I was somewhat prevented ; only in the liquor contained in their shells, I found 

 many small living animals ; and the muscle itself had two thin films, consisting 

 of long slender threads, with little knobby parts on them, something like the 



VOL. III. 3 Q 



