38 Dr. Waller on the Development of the 



tegration, 



where C may either be constant or a function of the time. By 

 putting JO = 0, we obtain the equation of the boundaiy of the 

 fluid, which thus appears to be at all times cylindrical. But 



since — = = -t-, by integrating, a?y = c^, and the lines of 



motion are thus shown to be rectangular hyperbolas. Hence if 

 the boundaiy be at one moment cyluidrical, it cannot be so the 

 next. Tims we have a third instance of contradiction indicative 

 of a logical fault. 



These three examples, which have been selected as being well- 

 adapted to illustrate the subsequent course of the reasoning, have 

 been long submitted to the consideration of mathematicians ; 

 and yet no one has hitherto shown that the steps of the processes 

 which have led to the contradictious are in any respect incon- 

 sistent with received hydrodynamical principles. I have been 

 unable myself, after devoting much attention to the subject, to 

 discover any such inconsistency, or to see any escape from the 

 conclusion that the received hydrodynamical principles are de- 

 fective. 



If, then, it be asked how the defect is to be supplied, I answer, 

 that the third general equation obtained in Proposition VI. must 

 be taken into account. The manner in which the diiSculty is 

 overcome by means of this equation wUl be the nex,t subject of 

 inquiiy. 



Cambridge Observatory, 

 Nov. 20, 1850. 



[To be continued.] 



V. On the Development of the Mouth and Tongue of the Frog. 

 By Augustus Waller, M.D."^ 



DURING the greatest part of the tadpole-life of the frog 

 there exists no trace of the tongue within the cavity of 

 the mouth ; and the mucous membrane which covers the body 

 of the hyoid bone and floor of the throat is quite smooth, and 

 destitute of any organization indicative of any special function. 



The apertui'e of the mouth at this period is of a triangular 

 shape, with jaws of a horny nature, and provided with a mem- 

 branous vestibule in front, which is closed by a kind of sphincter 

 oris, and is covered with numei'ous membranous folds having 

 several rows of minute black teeth fixed among them, besides 

 many conical-shaped papillae of a vascular nature. The labial 

 * Communirated bv the Author. 



