AT THE PHYSICO-TECHNICAL INSTITUTE 413 



day we discussed the monodromic axioms of spatial geometry, 

 Helmholtz having been very pleased with the explanation I gave 

 in the Math. Ann., vol. 37, p. 565, the relation of which to Lie's 

 own position I had discussed a little time before in Part II of my 

 Lectures on Higher Geometry. Next day Frau von Helmholtz 

 told me I must not discuss such hard problems with her husband; 

 it fatigued him too much/ 



In her letters to her daughter, Frau von Helmholtz gave a 

 lively account of the events of the American tour, to which Helm- 

 holtz contributed a few very interesting comments. 



' Thorwood, Dobbes Ferry, N. Y., August 19, 189$. 



1 If I did not know that it is we who are sitting here in an 

 ideal room above a mild English park-landscapelooking away 

 to the broad Hudson, on which white steamers pass up and down 

 like swans, with splendid trees, a lawn (that is not English, but 

 yellow) sloping downwards in front of the fine house, humming- 

 birds, real humming-birds, darting to and fro, and butterflies of 

 the same size ; that I have enjoyed a true water orgy here of 

 warm and cold baths; that yesterday morning we all huddled 

 together on the ship at 5 a. m. for breakfast, and landed without 

 any laurel wreaths or nymphs, or other appropriate reception, and 

 wrestled for two hours with our trunks, &c., I should not believe 

 it! Knapp came with his servant and coachman, and Clara 

 Gross was there, and Dr. Pringsheim with roses, and there was 

 a general bustle and leave-taking, and then we went in a kind of 

 covered ferry boat across an arm of the sea, and through half 

 New York, from the slums to the most beautiful quarter, to 

 Fifth Avenue, &c., till at last we found Knapp and this handsome 

 and very comfortable house as quiet as if one were in Carlton 

 Gardens, with everything at hand/ 



' Denver, Colorado, September 2, 1893. 



'Thirty hours across the prairies to get here from Chicago 

 was a great undertaking, after which we are having a whole 

 day's rest. Denver is a wonderful spot, 5,000 odd feet 

 above the sea, a city of palaces, villas and log cabins, with a 

 Capitol on the heights, of course, for the wise governors of 

 the State of Colorado and its silver mines. A villa quarter 

 of Norman castles, colonial farmhouses with huge verandas, 

 beautiful turf, trees, and some few flowers where the soil had 

 been irrigated : electric light, electric tramways, arena, boule- 



