Russell wrote a historico-philosophical [Essay on the Foundations of Geometry (1897)][1], which [Jost cites on p.127][2] and which is freely available on Gutenberg. Russell's reception of Riemann is already clear from the section titles concerning him:

> 60. *Riemann regarded space as a particular kind of manifold, i.e.
wholly quantitatively* 
61. *He therefore unduly neglected the qualitative adjectives of
space* 
62. *His philosophy rests on a vicious disjunction* 
63. *His definition of a manifold is obscure*
64. *And his definition of measurement applies only to space* 
65. *Though mathematically invaluable, his view of space as a
manifold is philosophically misleading*

Aside from showing that Russell was a little too harsh on Riemann what this makes clear is that his qualms were more philosophical than mathematical. It helps to remember that Riemann was a Kantian, he explicitly names Kant's successor at Königsberg, Herbart, as an influence in his lecture, the only other named influence is Gauss, see more in http://hsm.stackexchange.com/questions/657/which-school-of-philosophy-motivated-thinking-about-spaces-of-higher-dimension/673#673 And, [as we know from Russell][3], "*it was towards the end of 1898 that Moore and I rebelled against both Kant and Hegel"*, to found analytic philosophy. 

The Riemann's "*vicious disjunction*" is that "*either the axioms must be consequences of general conceptions of magnitude, he thinks, or else they can only be proved by experience*". In Russell's opinion, we must ask instead "*What axioms, i.e. what adjectives of space, must be presupposed, in order that quantitative comparison of the parts of space may be possible at all?*" And not asking that, to Russell, was Riemann's cardinal sin:

>*His philosophy is chiefly vitiated, to my mind, by this fallacy, and by the uncritical assumption that a metrical coordinate systern can be set up independently of any axioms as to space-measurement. Riemann has failed to observe, what I have endeavoured to prove in the next chapter, that, unless space had a strictly constant measure of curvature, Geometry would become impossible; also that the absence of constant measure of curvature involves absolute position, which is an absurdity.* 

What is most ironic about this is that the soon to be anti-Kantian Russell is criticizing Riemann for... not being Kantian enough. Namely, overlooking the constitutive  principles that have to be adopted a priori for empirical measurements to become possible. The reason Russell puts such a premium on constant curvature is that only with that is transitive metric-preserving action possible, and hence measurement in his 1897 opinion. And that of course is also a replication of Kant's similar thesis about the Euclidean geometry. Einstein would dispel such narrow views of physical geometry soon enough.

Jost recommneded commentary on Russell on Riemann is [Toretti's Philosophy of Geometry from Riemann to Poincaré][4], see also this year's [Space, Number, and Geometry from Helmholtz to Cassirer by Biagioli][5].




[1]: https://archive.org/details/117723764
[2]: http://download.springer.com/static/pdf/197/chp%253A10.1007%252F978-3-319-26042-6_5.pdf?originUrl=http%3A%2F%2Flink.springer.com%2Fchapter%2F10.1007%2F978-3-319-26042-6_5&token2=exp=1475439092~acl=%2Fstatic%2Fpdf%2F197%2Fchp%25253A10.1007%25252F978-3-319-26042-6_5.pdf%3ForiginUrl%3Dhttp%253A%252F%252Flink.springer.com%252Fchapter%252F10.1007%252F978-3-319-26042-6_5*~hmac=a7a539ad60183438d52915eaa86e6727279543068a49248af252cda83b0f429c
[3]: http://www.iep.utm.edu/analytic/#H1
[4]: https://books.google.com/books?id=EcLrCAAAQBAJ&source=gbs_navlinks_s
[5]: https://books.google.com/books?id=dSPkDAAAQBAJ&source=gbs_navlinks_s