the Value of different Alkalis. 91 



division with the test acid, drop so much into the sample, con- 

 stantly stirring the mixture, as will just change its green 

 colour to crimson ; the quantity of acid used, as indicated by 

 the divisions on the tube, will show the per centage of alkali 

 in the sample, if it be barilla, kelp, or manufactured soda ; but, 

 if the sample be pot or pearl ashes, augment the proportion of 

 test acid used, by adding to the number of divisions indicated 

 by the dropping tube, one half such number, and the total will 

 be the per centage of alkali in such sample. 



Should it be desired to ascertain the quantity of carbonic 

 acid contained in the sample, we need only note the point at 

 which the solution becomes blue in the foregoing process, and 

 deduct the divisions then indicated by the test tube from the 

 subsequent total amount ; every ten of the remainder will then 

 indicate seven per cent, of carbonic acid, whether of barilla or 

 of pot-ash. 



The apparatus is made and sold by Mr. Bate, Philosophical- 

 instrument Maker, 21, Poultry. 



Memoir on the Mean Results of Observations ; read before the 

 Academy of Sciences, April 20, 1829. 



By M. Poisson. 



This Memoir is the continuation of that which I inserted in 

 the Additions a la Connaissance des Temps for the year 1827. 

 My object is to add some new developements to that part of it 

 which treats on the probability of arithmetical means between 

 the results of a great number of observations. When there is 

 no reason for believing some more exact than the rest, the 

 mean of them should be taken for the unknown value sought ; 

 and one is naturally led to think that this mean result ap- 

 proaches the nearer to the truth as the number of the observa- 

 tions is more considerable. But La Grange is the first person 

 who subjected this question to mathematical analysis*, and 

 who investigated the probability that the arithmetical mean 

 between any number of observations does not differ from the 



* Vol. v. of the old Memoirs of the Academy of Turin. 



