CHANGES IN LENGTH OF DAY— BROWN 173 



The fundamental series have been the meridian observations at 

 Greenwich and Washington — in the former case an unbroken series 

 since 1750. In these observations the times at which the limb of 

 the moon crosses the wire in the transit meridian telescope is observed. 

 The declination is also noted by placing the cross-wire on the upper 

 or lower limb of the moon. By means of tables, given in the nautical 

 almanac, the position of the moon at those instants can be found. 

 Unfortunately, these observations are subject to many errors. There 

 are the instrumental errors, most of which can be dealt with; the 

 errors due to the irregular shape of the limb, for which corrections 

 can be made; and finally the error of the observer when he tries to 

 make the wire tangent to the limb. The last is the most serious 

 because it varies with different observers and with the same observer 

 at different times. About 100 obser stations a year are obtained in 

 this way at each observatory with some 50 more at Greenwich obtained 

 by noting when the wires cross the crater Mosting A. During the 

 last 12 years a campaign has been under way to obtain and utilize 

 occupations. Here we simply observe the instant when the moon 

 covers a star. There are practically no instrumental errors, and as 

 the time of occurrence need only be observed to the nearest second, 

 the human factor does not seriously enter. But they still depend on 

 the shape of the edge of the moon and, in addition, on the accuracy 

 of the places of the stars. Both of these errors can be largely cor- 

 rected so that the possibility for accuracy with this latter method 

 seems to be greater than with the meridian observations. It has been 

 possible also to obtain many more such observations. During the 

 3 years 1933-35, we had an average of over 1,400 a year. With all 

 this material we now know with considerable accuracy how the rate 

 of rotation of the earth is varying from year to year. It should be 

 mentioned that Newcomb got his original curve from occultations 

 which he gathered from all over the world. 



What is the cause of these variations in the earth's rate of rotation? 

 At present the answer is — we do not know. But the facts at our 

 disposal enable us to eliminate a good many hypotheses that mxiglit 

 otherwise have some plausibility and thus narrow the field of con- 

 jecture. Perhaps we may even go so far as to say that possibly we 

 can obtain new information concerning the behavior of our earth. 



The quantity we are mainly concerned with is the angular momen- 

 tum. This is a product of the angular velocity, the mass, the square 

 of the radius, and a constant which depends on the manner in which 

 the mass of the earth is distributed. Theory tells us that this cannot 

 be changed (except in a manner which is easily calculated and which 

 is allowed for). We have seen that there is one important exception, 

 namely, the frictional effect of the tides produced by the sun and the 

 moon. The irregular changes might be supposed to be due to varia- 



