542 PHILOSOPHICAL TKANSACTIONS. [anNO 1700-1. 



tonneken,* some of which are so thin and transparent, that I have often seen 

 their limbs and their numerous eyes distinctly within. Now if this figure and 

 parts of a fly were not actually included in the worm, such a transmutation 

 would have been inconceivable ; so it is also with the creature in the male seed ; 

 but it is impossible for any man to penetrate into the secret parts of such a 

 wonderful minute animal. 



If we should consider the tail of one of those aforementioned creatures, we 

 must needs be astonished at the incomprehensible number and smallness of its 

 parts, especially if we conclude that such a very small tail is provided with as 

 many joints in proportion as the tails of larger animals, otherwise it could not 

 move nimbly on every side as it ought to do ; and again, that every one of these 

 little joints consists not only of muscles, but also of arteries and veins, which 

 convey the nourishment down to it : when we consider this, and the smallness 

 of all the other parts of the body, we cannot sufficiently admire the wonderful 

 works of God. 



Part of a Letter to Dr. Sloane, containing Solutions to two Problems. 1. On 

 the Solid of least Resistance. 1. The Curve of quickest Descent. By the 

 Rev. John Craig. IN® 268, p. 746. Translated from the Latin. 



In the first part of this paper Mr. Craig assigns his reasons for wishing these 

 solutions to be published : observing, that Sir Isaac Newton had thought it 

 proper to conceal his analyses ; and that although some other eminent men, as 

 Bernouilli, and the Marquis De L'Hospital had exhibited solutions, yet he 

 hoped the simplicity of his investigation would recommend it ; and the sciences 

 might be farther extended in proportion as the same things were treated with 

 the greater variety. 



Lemma. To find the ratio between the resistances which the right angled 

 triangle aig, and the circumscribing rectangle AiGg, meet with in moving 

 through a fluid, according to the direction of the line ia, from i towards x. 

 PI. 13, fig. 1. 



To any point B in ag let the perpendicular bc be drawn, and sb parallel to 



Ai, likewise em perpendicular to ai. Also in bB take bn = — , and bs = 



BC : through the points h, e, draw the right lines ha, ea, which produce till 

 they intersect eg in k and f : then the resistance of the triangle aig will be to 

 the resistance of the rectangle AiGg, as the area of the triangle akg, to the 

 area of the triangle AFg. And the resistance against any part taken at pleasure 

 in the line ag, to the resistance against the corresponding part of the line Ag, 

 for example, against ab and ab, as the area ahb to the area AEb. The demon- 



* Chrysalis. 



