736 J. A. BROUN ON THE LUNAR DIURNAL VARIATION OF 



lunar diurnal variation, no conclusions had been drawn either as to the way in 

 which the law varied in passing from one hemisphere to another, or as to the 

 way in which it might change near the equator with the position of the sun or 

 moon in declination. As nothing is known as to the mode in which the sun 

 and moon produce these variations, nothing could certainly be predicted a priori 

 as to the change of the law under the circumstances just mentioned. 



4. The first result obtained from a discussion of observations made during 

 the five years 1854 to 1858 at Trevandrum, was that the law of lunar diurnal 

 variation for the group of months about January was the inverse of that for the 

 months about July.* This fact, which held also for the solar diurnal variation, 

 appeared to relate both variations to the position of the earth in its orbit, rather 

 than to the passage of the sun from one hemisphere to the other. The similarity 

 in the change of the law of lunar and solar diurnal variation for the sun north 

 and south of the equator, led also to the conclusion that the mean lunar diurnal 

 movement, like the mean solar diurnal movement, should be in opposite direc- 

 tions in the high latitudes of the two hemispheres : the facts have since then 

 been found to be in accordance with this conclusion.t 



5. The next question of importance was, whether the moon's passage from 

 one hemisphere to the other would produce any marked change in the law of 

 variation, or in its amount. The discussion of five years' observations seemed 

 to show a considerable difference in the relative magnitude of the maximum 

 and minimum, not only with the moon farthest north and south, but also with 

 the position of the moon on the equator, according as she was moving towards 

 the north or towards the south. 



6. As the action of the moon on the needle may vary from different causes, 

 it becomes necessary, to be sure in obtaining the results for any given argument, 

 that we have got rid of the effects dependent on other arguments. 



If we assume, in the first instance, that the solar diurnal variation is the 

 same for each day throughout a month, and that a similar supposition holds for 

 the moon ; then, as in a month, which is nearly equal to a lunation, the moon 

 will have been on all the twenty-four meridians at each of the solar hours, the 

 mean disturbing action of the moon will have been the same at each of the 

 solar hours, and the mean position of the needle for each solar hour, as derived 

 from a month's observations, will be equally affected or unaffected by the lunar 

 action.! A similar conclusion may be arrived at relatively to the mean position 

 of the needle for the- moon on different meridians : thus, if all the observations 

 made during a lunation for the moon on the principal meridian be summed 



* Proceedings of the Royal Society of London, vol. x. p. 475. 1861. 



•f" Proc. Roy. Soc. Lond., vol. xvi. p. 59. 



% Hence the mean solar diurnal variation sought, in any case, from fewer than a month's observa- 

 tions will be more or less in error, according as the lunar action (and the change of its law during the 

 lunation) is more or less considerable 



