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length of the needle had no sensible influence upon the extent of its 

 deviations. In order to determine this point, he began by ascertain- 

 ing more scrupulously than had yet been done, the values of several 

 of the elements of the calculation, such as the exact positions of the 

 points where the intensity of the magnetism is the greatest, and also 

 of the point of neutrality, or of the magnetic centre ; and he next 

 subjected to a more severe scrutiny a law which had been regarded 

 as established by experiment ; namely, that the tangent of the devi- 

 ation is proportional to the rectangle of the cosine of the longitude, 

 into the sine of the double latitude of the position of the centre of 

 the needle, with relation to the mass of iron as referred to a hollow 

 sphere. 



In the course of his experiments the author ascertained that if any 

 bar of steel, uniformly magnetized by the method of double touch, 

 have this state of magnetism disturbed by drawing the end of a mag- 

 net from its centre to the end, having the same polarity as that ap- 

 plied to it, then the pole at that end will be shifted towards the 

 centre, while the opposite pole will be removed further from it, and 

 a corresponding change will occur in the position of the magnetic 

 centre. Changes will also take place in the absolute intensities of 

 the magnetism at each pole. Considerable differences were observed 

 in the extent of the deviations of a needle six inches in length, and 

 of one of two inches long, when successively placed in the same po- 

 sition with relation to the shell of iron. At the distance of 16' 8 

 inches they amounted to more than two degrees and a half; and the 

 difference continued to be very sensible even at a distance of 24 inches 

 from the shell. In general when the needles were near to the north 

 or south of the centre of the shell, the deviations of the longer needle 

 exceeded those of the shorter ; and the reverse took place when the 

 needles were placed on the east and west sides. Hence he concludes 

 that the efficacy of a small mass of iron placed near to the needle to 

 serve as a compensation to the effects of more distant masses, will 

 depend upon its being itself at such a distance from the needle as 

 that the difference of its action upon a long and a short needle shall 

 be insensible. 



The author proceeds to deduce from the law which he has pro- 

 posed various forms of equations for determining the deviations of a 

 horizontal-needle due to the action of an iron sphere or shell appli- 

 cable to different circumstances and conditions of the case. In one 

 set of equations, actions and resulting positions are referred to three 

 rectangular co-ordinates proceeding from the centre of the needle ; 

 and in another set they are referred to polar co-ordinates relative to 

 the vertical and to the plane of the horizon. He next deduces equa- 

 tions for computing the deviations of a needle in which the mag- 

 netism has been disturbed by applying to one of its poles the corre- 

 sponding pole of a magnet. He then proceeds to the detail of ex- 

 periments for investigating the above-mentioned laws, and to their 

 comparison with the results deduced from theory. These experi- 

 ments appear to him to establish, beyond all doubt, the influence 



