Mr. Robberds in reply to Mr. R. C. Taylor. 271 



the caustic is a logarithmic spiral similar to the refracting 

 curve. 



If in the equations we have thus deduced for the involute to 

 the caustic by refraction, {m) be made equal to unity, we shall 

 at once determine the involute to the caustic by reflexion. 

 Thus for rectangular coordinates, we have 



X3 + Y-2 - 2Xx - 2Yy = («) 



Yy + X=_0 (/3) 



Or, to determine the curve in terms of R and P, we have 



p = 7" H 



R = 2P (/3)' 



From these last equations it w^ill be easily seen that the in- 

 volute to the caustic by reflexion, is in fact the curve which 

 would be traced out by a point similarly situated with the ra- 

 diating point in a curve similar and equal to the reflecting 

 curve made to roll on its circumference, similar points having 

 first been in contact, and both curves being in the same plane. 



XLV. Reply to Mr. R. C. Taylor's Remarks on the Hypothesis 

 of Mr. Robberds on the former Level of the Germati Ocean. 

 By J. W. Robberds, Esq. Jun. 



[Continued from p. 207.] 



A FTER admitting the general validity of the evidence, 

 -^^^ which I have adduced from historical facts, and from 

 the names of several places on the verge of these valleys, 

 Mr. Taylor has objected to the accuracy of some minor points, 

 which do not materially affect the main argument. I acknow- 

 ledge readily the error into which I was betrayed, respecting 

 Waybridge. As I could find no village bearing that name on 

 either of the three rivers, I too incautiously adopted Gilling- 

 water's version of it, who, in his History of Lowestoff, p. 27, 

 rendered it Weybread, without even mentioning the real name 

 given by Swinden. Mr. Taylor calls mine a ^'■mistaken quota- 

 tion." This is not correct ; for I quoted the word right, but 

 explained it wrong, having cited it as " Waybridge (the pre- 

 sent Weybread)." The bridge at Acle, so designated, may 

 have existed in the eleventh century, without affording any 

 conclusive proof of the fallacy of my inference from more ge- 

 neral and uiK[uestionable liicts. I much wish that Mr. Taylor 

 had given his authority for that statement. In the earliest ac- 

 count of the priory founded there in the reign of Edward L, 



it 



