1877.] 



the Lines of equal Bai^ometric Pressure. 



521 



The probable errors are here sufficiently small, when compared with 

 the variations from group to group, to allow us to conclude that we 

 have obtained a considerable approximation to the law o£ change for the 

 centre of England. It is not a little remarkable that the greatest 

 monthly mean pressure (that for September) is followed immediately by 

 the least, the probable errors leaving no doubt as to this fact*, the 

 difference of pressure from September to October-November being 

 0*173 inch. It is not improbable that the pressure in December is 

 greater than in the months immediately following ; but a longer series of 

 observations is required to determine that question, since the probable 

 error for the month is very large. 



The mean barometric pressure at the mean sea-level for a point in 

 53° 24' N. and 2° 48' "W. of Greemvich is 



29-897 inch + -010, 



as deduced from the eight years' observations (1842-49) at the three 

 stations. 



Annual Variation of tlie quantities ^- — It will be seen from 



Table V. that the magnitude of and /S^ is a maximum in December 

 and January, a minimum in April or May, a secondary maximum in 

 July, and a minimum again in September. This result was obtained 

 by me for in 1850. The perpendicular distances between the isobars 

 calculated with the aid of the values of Q are given in the last column of 

 Table Y. : the distances are least about January and about July ; they 

 are greatest in April, May, and September. The following are the 

 differences of barometric pressure corresponding to 100 geographical 

 miles perpendicular to the isobar. 



* The probable errors given above and in Table V. have been obtained in the same 

 way as for the observations of a constant quantity. There can be no doubt, however, 

 that the conditions are not strictly the same in the two cases. In the case of devia- 

 tions of observations of magnetic declination from the mean, I have shown, in the 

 Makerstovm Observations for 1844 (Trans. Eoy. Soc. Edinb. vol. xviii. p. 351), that 

 they did not satisfy the hypothesis of positive and negative- distributiou employed in 

 the calculus of probabilities for the probable error. This is also true for various 

 meteorological phenomena. A consideration of the differences of the monthly mean 

 barometric height has induced me to beheve that the formula for the probable error 

 ^ives such an approximation to the probable deviation of any determination that it 

 may be accepted as a relative measure of the exactness of the result. It will be obvious 

 also that these differences cannot be called errors if they are due to a law. In the 

 present instance it has been remarked that j8„ jS.,, and seem all to have a somewhat 

 regular variation depending on the year. It will be seen, however, from the last Une 

 of Table V., that if we assume this variation to be accidental, the probable difference 

 due to it is so small that it can only shghtly increase the probable differences or 

 errors for the different months. 



