Referee's report by William Burnside, on a paper 'The differential invariants of space' by Andrew Russell Forsyth Sectional Committee: Mathematics Recommended for publication in Philosophical Transactions. The present paper forms a sequel to Burnside's former memoir on the differential invariants of a surface, which has already been accepted for publication in Philosophical Transactions. It should 'certainly' be printed in full as the author has omitted the more laborious of the calculations and given the results only. Discusses a statement on page one that should be omitted as it might give a reader an incorrect idea of the problem discussed in the paper. Outlines what a true generalization of the author's previous memoir would involve. [Published in the Philosophical Transactions A, 1904]. Endorsed on verso as received 6 July 1903. July 1903