312 Mr Ibbetson, On an elastic shell. [May 25, 



Another distinction is between real and fictitious or subjective 

 means (the latter belonging to statistics in so far as distinguished 

 from observations). There is a real mean in the ordinary case of 

 a physical quantity elicited from observations. A subjective mean 

 is of this nature. In the case of fluctuating phenomena, e.g. prices, 

 we may select a certain value (not as that of a real thing, but) as 

 the best representative of the whole set; which, if we must put 

 one for many, minimizes the detriment incidental to that neces- 

 sity. The subjective mean is found by a mathematical process 

 analogous to Laplace's reasoning at p. 333, Theor. Anal. 3rd ed. 

 (p. 365, Nat. ed.). In the case of a simple facility-curve this mean 

 is the central point, other in other cases. 



Laplace's theory in the passage cited is defended as the most 

 philosophical view of the problem of observations. In fact, though 

 we begin with the search of a real point — namely that from which 

 observations have emanated — we have to take as a proximate end 

 a certain subjective mean. When we have found by inverse pro- 

 babilities the relative frequency with which different points 

 originate the given observations x x , x 2 , % 3 ..., we seek the subjec- 

 tive mean of the set of values found. 



The nature of a subjective mean explains Laplace's conception 

 of the " most advantageous " as distinguished from the " most pro- 

 bable " value. 



It is attempted to elucidate many other vexed passages in 

 Theorie Analytique, e.g. the method of situation, the proof offered 

 in the second supplement of the accui'acy of the method of least 

 squares, the assumption of mean error as test of advantage, &c. 



The paper is being printed in full in the Transactions of the 

 Society. 



Note on Mr Ibbetson's paper " On the free small normal 

 vibrations of a thin homogeneous and isotropic elastic shell, bounded 

 by two confocal spheroids. Communicated Jan. 28, 1884. Cor- 

 rection by the author. 



The expression assumed on p. 70, line 19, for the thickness t 

 of the shell at (tj, £), supposes the tangent planes at the points 

 on the outer and inner surfaces of the shell having these co- 

 ordinates to be parallel. It is in fact the formula appropriate to 

 a shell bounded by similar spheroids. 



The correct expression for t for confocals is 



_ g _ f i 

 T [AJ " 2ac • V*- 



