MATHEMATICS AND NATURAL PHILOSOPHY. 459 



at a third station, St. Helena, which is a tropical oDe, the hours of principal dis- 

 turbance are those not of the night, but of the day. A very superficial examina- 

 tion is sufficient to show that for the generalization of the facts, — a .generalization 

 which is indispensable for their correct apprehension and employment in the form- 

 ation of a theory, — the stations at which the phenomena are to be known must be 

 increased. Those which were chosen for a first experiment were well selected to 

 prove the importance of the investigation, aud thus to lead to its extension. It 

 is only at the Colonial Observatories that the disturbance-variations have hitherto 

 been made out; and taking experience as our guide, we have before us the evi- 

 dence of the means by which the inquiry may be further successfully prosecuted. 

 Periodical Variations. — The anticipation expressed in the Report of the Com- 

 mittee of Physics, that for the purpose of obtaining a correct knowledge of the 

 regular periodical variations, it would be found necessary to eliminate the "casual 

 perturbations," has "been fully -confirmed. Had the latter been strictly " casual" 

 (or accidental, in a sense contradistinguished from and opposed -to periodical), a 

 sufficiently extended continuance of observation might haye occasioned their mu- 

 tual compensation ; but now that we have learned that the mean effects which they 

 produce are governed by periodical laws, and that these laws and those of the re- 

 gular periodical variations are dissimilar in their epochs, it is manifest that in 

 their joint and undivided effects we have two variations, due to different causes 

 and having distinct laws, superimposed upon each other ; to knoio the one correctly 

 we must necessarily therefore eliminate the other. A striking illustration of the 

 importance of such elimination is furnished by the solar-diurnal variation of the 

 total force. It will readily be imagined that the question must be an important 

 one, whether a variation, which is supposed to derive its origin from the sun, be a 

 single or a double progression ; whether it have two maxima and two minima in 

 the twenty-four hours, or but one maximum and one minimum in that period. 

 When no separation is made of the disturbances, the progression appears to be a 

 double one, having two minima, one occurring in the day and the other in the night. 

 With the removal of the disturbed observations the night minimum disappears, 

 and we learn that the regular 6olar-diurnal variation of the total force has but one 

 notable inflection in the twenty-four hours, viz., that which takes place during the 

 hours when the sun is above the horizon. The night minimum is in fact the mean 

 effect of the occasional disturbances. It is probable that the nocturnal inflection 

 of the solar-diurnal variation of the Declination may be ascribed to the same 

 cause, namely to the superposition of two distinct variations. 



A careful analysis of the solar-diurnal variations of the Declination at the Co- 

 lonial Observatories has brought to light the existence at all these stations, of an 

 annual inequality in the direction of the needle concurrent with changes in the 

 sun's declination, having its maxima (in opposite directions) when the sun is in or 

 near the opposite solstices, and disappearing at or near the epochs of the equinoxes. 

 An intercomparison of the results of the analysis at these stations has shown, that 

 this inequality has the remarkable characteristic of having notably the same di- 

 rection and amount in the southern as in the northern hemisphere, and in the tro. 

 pical as in the temperate zones. An ingenious explanation of the phenomena 

 has been suggested by Dr. Langberg 'of Christiana (Proceedings of the Royal 

 Society, vol. vii., p. 434) ; but whether this explanation be or be not the correct 

 one, the theoretical importance of the facts cannot be doubted, inasmuch as they 

 appear to be wholly irreconcileable with the hypothesis which would attribute the 



