46 report— 1879. 



University, Columbus, Ohio, to be used for observing the temperature at 

 every 100 feet of depth during the sinking of a shaft, probably to the 

 depth of about 4500 feet, in one of the mines of the Comstock lode in 

 Nevada. Two others have been supplied on similar terms to the 

 Meteorological Office. 



With the view of carrying out the resolution, expressed in last year's 

 Report, to commence thermo-electric observations in filled bores, the 

 Secretary has procured from Messrs. Siemens 500 feet of No. 20 copper 

 wire, and the same length of No. 19 soft charcoal iron wire, both of them 

 well insulated with gutta-percha, and has conducted some thermo-electric 

 experiments with them in the Laboratory ; but the apparatus is not yet 

 ready for actual use. 



Mr. Lebour has improved the form of plug devised by him (on the 

 umbrella principle) mentioned in previous Reports (1876, p. 209, and 

 1877, p. 199). The apparatus now requires only one wire, and remains 

 collapsed so long as the wire is taut, but opens out and plugs the hole 

 when it becomes slack. 



The following corrections are to be made in last year's Report. 



In the acount of Dr. Stapff's thermometers, ' steel cap ' and ' steel 

 jacket,' should be ' brass cap ' and ' brass jacket.' 



At a later place in the extract from Dr. Stapff's paper, • wet bore- 

 holes with standing water,' should be ' wet bore-holes with running 

 water.' 



In the references to papers, in foot-note, ' 1878, 1876, and 1877,' 

 should be ' 1875, 1876, and 1877.' 



Report of the Committee, consisting of Professor Catlet, F.R.S., 

 Professor G. G. Stokes, F.R.S., Professor H. J. S. Smith, F.R.S., 

 Professor Sir William Thomson, F.R.S., Mr. James Glaisher, 

 F.R.S., and Mr. J. W. L. Glaisher, F.R.S. (Secretary), on Ma- 

 thematical Tables. Drawn up by Mr. J. W. L. Glaisher. 



[Plate I.] 



The present report consists of two parts : I. An account of the state of 

 the calculation of the factor tables for the fourth, fifth, and sixth millions, 

 with some results of the enumeration of the primes in the fourth million ; 

 and II. Tables of the Legendrian functions, with an introduction. 



I. — State of the Calculation of the Factor Tables for the Fourth, Fifth, 



and Sixth Millions. 



During the year the calculation has been carried on without inter- 

 mission under the direction of Mr. James Glaisher. At present the 

 factor table for the fourth million is printed and stereotyped, and will be 

 published immediately ; the manuscript of the fifth million is complete 

 and ready for the printer. In the sixth million all the entries by sieves 



