On the Constant P in Observations of Terrestrial Magnetism

Abstract

I AM afraid that the new method of calculating P₀ adopted by Prof. Harkness is not less arbitrary than that which he previously employed. He says that “P₀ must be determined so as to make L′ and L″ as nearly as possible identical with L.” If the object is only to deduce a correct value of L by combining equations (15) and (16), this condition is certainly not necessary. For if we substitute from (17) in (15) and (16), and take the mean of the values of L′ and L″, we get by a very roundabout process the same value of L as we should have obtained without using P₀ at all. But we should have reached the same final result if we had started with the assumption that (n + m) L = n L′ + m L″, where n and m are any numbers whatever. By properly choosing n and m we could deduce the correct value of L with any assigned value of P₀. It appears to me that the equation 2L = L′ + L″ is based upon the tacit assumption that L′ and L″ are to be combined in accordance with the rules applied to fallible measures, and cannot otherwise be justified if the only object is the correct deduction of L from (15) and (16).