OF ARTS AND SCIENCES. 39 



since t =^ r very nearly. When, however, t — r becomes sufficiently 

 large, the value of t as computed by the second expression must be 

 considered as a first approximation only, and a second or third must 

 le computed. 



Without entering into the further discussion of thermometry which 

 I have made, a portion of which was presented in a paper (unpub- 

 lished) read at the Boston Meeting of the American Association for the 

 Advancement of Science in 1880, I will assert that the errors in my 

 thermometric work are below the values assigned to A < in Table VIII. 



In order to determine the deviation of the mercurial thermometers 

 used in my measurements from the air thermometer, a direct compari- 

 son was made of these and several others, the results of which possess 

 some interest, and will be here given. 



Through the kindness of Prof. H. A. Rowland, to whom I would 

 here express my sincere thanks for his courtesy and assistance, and 

 by an appropriation granted by the Rumford Committee of tlie Ameri- 

 can Academy, I was enabled to visit Baltimore in January, 1879, and 

 to make, in co-operation with Prof. Rowland, some thermometric com- 

 parisons, using an apparatus designed by him. 



The method and apparatus for comparisons at temperatures below 

 100° C. were those described and discussed in full by Prof. Rowland 

 in his valuable memoir on the Mechanical Equivalent of Heat.* It is 

 unnecessary to reproduce the description here further than to say that 

 a water bath was used in the apparatus, that the whole thermometer 

 was immersed, and that in the discussion of the accuracy of the ap- 

 paratus Prof. Rowland writes, f " From this table it would seem that 

 there should be no difficulty in determining the 40° point on the air 

 thermometer to at least 1 in 2000 ; and experience has justified this 

 result." It is quite possible, however, that the result obtained in my 

 comparison was not of quite as high precision as this, but it did not fall 

 far short. 



On two successive days a group of four thermometers was compared 

 with the air thermometer, with the results shown in the two follow- 

 ing tables. Thermometer Baudin G1G3, whose error had already 

 been carefully studied by Prof. Rowland, was included in both series. 

 Table IX., on page 38, gives the complete description of the various 

 instruments. Casella 32378 was used in my measurements below 

 100°. It is a fairly good instrument, but decidedly inferior to any of 



* Tiiese Proceedings, June, 1879, vol. xv. pp. 77 et seq. 

 t Ibid., p. 99. 



