Bulletin of the Calcutta Mathematical Society 1916

The object of this paper is to study in a number of typical eases the question of the existence of the second derivates of the Newtonian potential due to a volume distribution ihaving a discontinuity of the second kind. [...] And it is to the great German mathematicians of the 15th and 16th centuries George Purbach John Mueller (Regimontanus) Michwl Stifel and George Joachim (Rheeticus) that we owe those great developments of the Science and Art of computation which made it such a powerful instrument in the study of the heavens and a material help to the labours of the great astronomers of the sixteenth century. [...] Thus from the logarithm of the last term in the First Table we pass by means o(5) to the logarithm of the Second term in the Second Table and we find by taking the A. M. of the limits given by (5) the logarithm to be 100.0005000. [...] This then is the common difference of the logarithms of the twenty-one numbers in the first column of the Third Table which are in G. P. We obtain thus the logarithm of the last number in the first column of the Third Table and the passage from that to the logarithm of the first number of the second column is easy and the latter is found to be 100503.358. [...] 35 divisors of A the factors of D are called the maximnm diri.s'ors of A of order i ; and if E is expressed as a product of powers of irreducible divisors of A the factors of E are called the potent divisors of A of order i The last three sets of quantities all have reference to some (usually the smallest possible) domain of rationality 12 in which all the elements of A lie an irreducible func