472 EEPOKT— 1882. 



picked for uniformity of curvature. Occasion all j', with a favourable adjustment, 

 he had divided b^ with it in the fifth spectrum ; to do this the vertical aperture had 

 to be diminished, but not the horizontal. 



He did not know what the limit to the closeness of ruling which can be performed, 

 by the machine is, but it depends more on the diamond and the surface ruled on 

 than anything else. He had had no difficulty in ruling small areas with 100,000 

 lines per inch, and although he had no microscope objective which would show lines 

 as close as this, their presence could be detected by the blue gleam of the light 

 diffracted by them when held very obliquely in the sunlight. 



At the rate at which he had hitherto worked the machine, viz., about 4 lines 

 per minute, it would take several weeks to rule a C grating of 20,000 lines per 

 inch, and in view of these long periods, during which the temperature of the 

 machine ought not to vary, it has been placed in a double room, one completely 

 enclosed within the other, and apparatus added for automatically keeping the 

 temperature constant. 



Self-registering thermometers which record the temperature of the machine 

 room and the outer air show that even when the latter varies from 15° to 18° 

 Fahr., the former does not vary more than two or three tenths ; a result which he 

 thought may be considered very satisfactory. 



He hoped, however, to be able to increase the speed of working very consider- 

 ably, the limit to which can of course only be found by trial. 



7. A Numerical Estimate of the Rigidity of the Earth. 

 By G. H. Daewin, F.E.S. 



About fifteen years ago Sir "William Thomson pointed out that, however it be 

 constituted, the body of the earth must of necessity yield to the tidal forces due ts 

 the attraction of the sun and moon, and he discussed the rigidity of the earth 

 on the hypothesis that it is an elastic body. 



If the solid earth were to yield as much as a perfect fiuid to these forces, the 

 tides in an ocean on its surface would necessarily be evanescent, and if the yielding 

 be of smaller amount, but still sensible, there must be a sensible reduction in the 

 height of the oceanic tides. 



Sir William Thomson appealed to the universal existence of oceanic tides of 

 considerable height as a proof that the earth, as a whole, possesses a high degree of 

 rigidity, and maintained that the previously received geological hypothesis of a 

 fiuid interior was untenable. At the same time he suggested that careful observa- 

 tion would afford a means of arriving at a numerical estimate of the average- 

 modulus of rigidity of the earth's mass as a whole. The semidiurnal and diurnal 

 tides present phenomena of such complexity, that it is quite beyond the power of 

 mathematics to calculate what these heights would be, if the earth's mass were 

 absolutely unyielding. But the tides of long period are nearly free from the 

 dynamical influences which render those of short period so intractable to calcidation, 

 and must in fact nearly follow the laws of the ' equilibrium theory.' 



In 1867 it was not, however, even definitely known whether or not the tides of 

 long period were of sensible height at any station. Although there has been a con- 

 tinual advance in the knowledge of tidal phenomena since that time, it is only 

 within the last year that there is a sufficient accumulation of tidal observations,^ 

 properly reduced by harmonic analysis, to make it possible to carry out Sir William 

 Thomson's suggestion. The great advances in knowledge that have been recently 

 made are principally due to the adoption of systematic tidal observation at a great 

 number of stations by the Indian Government. The results of these observations 

 are now being issued yearly by the Secretary of State for India in the form of tide- 

 tables for the principal Indian ports. The author had had the pleasure of carrying 

 out the examination of the tidal records, and a detailed account of the work will 

 appear at § 848 of the new edition of Thomson and Tait's ' Natural Philosophy,'" 

 now in the press. 



The tides chosen for discussion were the lunar fortnightly declinational tide, 

 and the lunar monthly elliptic tide. These tides must be free from the meteoro- 



