of the Earth's Crust. ° 421 



lislicd by the Roj'al Irish Academy, and aftcrwai'ds making an 

 assumption inconsistent with that differentiation ? 



2. ^Vhat is the vahie of attempts made hitherto to determine 

 tlie thickness of the earth's crust ? 



The first question is purely personal,, and^ as such, not suited 

 to your Journal; but inasmuch as it affects my competence to 

 discuss the second or scientific question, I am bound to notice it. 



In the paper referred to, I obtained a certain equation (12), 

 derived from the attraction of the solid crust of the earth, com- 

 posed of layers following any continuous law of density and ellip- 

 ticity; from the attraction of a fluid nucleus, composed of layers 

 following auy law whatsoever, either the same or different, but 

 also continuous, of density and ellipticity; and from centrifugal 

 force arising from the rotation of the earth. The question is. 

 Have I a right to differentiate such an equation without, by 

 such differentiation, tacitly assuming the sameness of the laws of 

 density and ellipticity in the solid crust and fluid nucleus* ? I 

 believe that I have a right to do so, because the law of density 

 and ellipticity is continuous in both the fluid and solid part of 

 the earth, though it may be supposed diffei'ent in both. 



This question is one which turns on the metaphysics of the 

 calculus ; and though I felt confident I had made no mistake iu 

 differentiating this equation, yet I thought it right to lay the 

 j)oint before a mathematical friend, the Rev. Professor Jellett, on 

 whose skill and judgment in such matters I have a well-founded 

 confidence. He has favoured me with the following statement 

 which he permits me to publish, and from which it appears that 

 lie coincides with me in opiuiou : — 



"The question at issue between Arcluleacon Pratt and Prof. 

 Haughton may be stated generally as follows. An equation of 

 the form 



Y{u,y, \udx, \vdx)—0, .... (A) 



Jo J a 



is given. The quantities y, ti, v are determined by the equations 



y=fi[^)> u=<^^{x), v=fi{x) 



from ar = to x = l^, and by 



y=Mx), u = (l>c,{x), v=f^{x) 



from x:=h to x = 'd. Required to determine the rule for differ- 

 entiating this equation with regard to «, or in other words, to 



''• I licrc give the etiuatioii in question : — 



ef« „ 1 C%l.ah' «■■('" cle M«^f" „ ^ 



J ^0 *-'a t-'o 



