The Adjustment of Observations. 217 



As a result o£ this, fine mad beds are not easily eroded, 

 whereas coarser sand is easily moved. 



(b) Colloidal suspension and plasticity in gels becomes o£ 

 importance when the weight of! the particles is about equal 

 to one inter-molecular cohesion bond (e. g. with cubic 

 particles, s. g. 2'5, each has a diameter 



d= V (2-5-1)981 = 9 * 10 " 4cm ')' 



This agrees with the dimension usually assigned as a 

 maximum to colloidal particles. 



XXIV. The Adjustment of Observations. 

 By R. Meldrum Stewart *. 



IN a recent article f on this subject, Dr. Norman Campbell 

 describes a method of reduction o£ observations which is 

 proposed to replace the " method o£ least squares." Among 

 other statements ot* a similar tenor, it is claimed that the 

 latter is " an intolerably cumbrous method lor obtaining 

 quite misleading results," and that the method proposed " is 

 incomparably simpler and gives results which are not mis- 

 leading " ; and the intention is expressed of attempting to 

 entirely subvert the method of least squares. In the 

 interests o£ mathematical accuracy, and to prevent the 

 acceptance without due examination of misleading theory, 

 it does not seem right that such statements as these, and 

 such reasoning as occurs in parts of the above article, should 

 be allowed to pass unchallenged. 



The ;4 method of least squares " is based on two funda- 

 mental postulates, neither of which appears to be questioned 

 bv Dr. Campbell: (1) that the probability o£ the occurrence 

 of an error of any given magnitude is a function o£ that 

 magnitude ; (2) that in the case o£ several observations 

 to determine a single quantity, made under the same con- 

 ditions, the arithmetic mean is the most probable value of 

 the quantity sought : these postulates are the mathematical 

 equivalent of the Gaussian law of errors. Whether or not 

 this law of errors, and therefore these two assumptions, 

 be strictly true or not, is a question which it is not proposed 

 to argue at present ; the result of experience, however, 

 shows the law to be at least a close approximation to the 



* Communicated by the Author. 

 t Phil. Mag. February 1920, p. 177. 

 Phil. Mag. S. 6. Vol. 40, No. 236*. Aug. 1920. Q 



