12 PRESIDENTS ADDRESS. 



Magnitude Number 



I2.0 1,660,000 



13.0 3,680.000 



14.0 7,650.000 



15.0 15,500,000 



16.0 29,500,000 



17.0 54,900,000 



So actually, the Franklin-Adams ])lates locate for reference at 

 any time about 100 million stars, and these may be said to be all 

 the stars known to astronomers. Sj^ecial plates taken with the 

 largest telescopes indicate a much larger number of stars — per- 

 haps 10 to 15 hundred million in all. It will he noticed that 

 the ratio from one magnitude to another, which is larger than 3 

 at the beginning of the talile, i)rogressively decreases, and is 

 already less than 2 for the 15-16 magnitude; hence the authors 

 conclude 



That modern photographic telescopes penetrate to a distance at which 

 the stars begin to thin out fairly quickly either really or by absorption. 



Variation of Latiti'de. 

 Since March, 1910, and until December. 1914. the Union 

 Observatory has, aided for some years by a subsidy from the 

 International ( ieodetic Bureau, taken part in a scheme of obser- 

 vations for measuring the variation of latitude. I must be 

 brief, and will only say that the question at issue was : " Is this 

 variation common to the whole globe, or is it in part or wholly 

 due to the elasticity of the Earth, so that the deformation in 

 the northern hemisphere might be ditt'erent from that of the 

 southern hemisphere?" The result of our observations to 

 March, 191 3, proves that in the variation of latitude the Earth 

 moves as a solid. In Dr. All^recht's own words : — 



From this series of observations we can deduce an interesting con- 

 lirmation of the result, previously obtained, that the values of the quanti- 

 ties x, y. and c deduced from observations made in the northern hemi- 

 sphere, can be applied without any modification to the variation of the 

 latitude in the southern hemisphere.* 



Gravitation. 

 For upwards of half a century it has been known that the 

 law of gravitation seems to be insufficient to account for all 

 the i^lanetary motions — the most conspicuous exception being 

 the motion of the perihelion of Mercury's orbit — and it has 

 been found more recently that it is impossible to reconcile the 

 Moon's motion with gravitation. Recently Professor Larmor 

 and Mr. H. Glauert have proved that a certain amount of these 

 irregularities are due to variations in the length of the day; 

 Glauert finding that the length of the day has increased by a 

 hundredth of a second in a third of a century. This means 

 that as compared with a third of a century ago, the year will 

 appear to be about 3^/^ seconds longer. Such a change, be- 

 cause of our methods of determining time, will be most clearly 

 reflected in the motion of the ist Satellite of Jupiter, whose 

 eclipses can be observed with an accuracy of about i second, 



* Rapport sur les Travaux dii Bureau Central en 1914, page 6. 



