324 



to be placed in our results. A quantitative statement in any branch 

 of physical science should give, along with the numerical x*esult, the 

 limit or probability of error, and conclusions drawn from such num- 

 bers ought to be made with the probabilities of error full in view. 

 Increased exactitude is only to be obtained by improvements in the 

 means of observing. 



The subject may be presented in another light. Assuming that 

 there is some unknown influence tending to derange our otherwise 

 •perfect observations, we may try to obtain some estimate of its 

 amount. If we were to take the errors as indicating the intensity 

 of the influence, the sum of these errors being zero when the 

 mean is assumed as true, would give zero for the entire influence, 

 hence we must take, with Legendre, the square of the error as 

 the measure of intensity. In this way, the sum of the squares 

 of the deviations from the mean may represent the entire force 

 of the deranging influence, and thence the deranging influence on 

 one observation may be estimated. Following this mode with 

 Santini's latitudes, we find 3"*34 as the probable error ; but 

 whether this is to be regarded as the probable error of all, or of one 

 of the observations, is not very clear : indeed the whole doctrine is 

 hypothetical. If we grant the soundness of the method of minimum 

 squares, it is easy to show that the probable or possible error of the 

 result is about three-tenths of the ultimate division of the apparatus. 



The following Gentleman was elected an Ordinary Fel- 

 low : — 



Dr Wright, F.G.S., of Cheltenham. 



