On the Jacobian of the Primary Minors. 507 



is rigidly connected with the end of the axis y y. At b there 

 is a bevel-wheel connected to the stationary base of the 

 instrument; at b l there is a similar wheel, having an equal 

 number of teeth, fixed to the axis x x. At c there is an oil- 

 reservoir for lubricating the bearings. A flexible thin-wire 

 cable is used as a connector ; this is at one end joined to a 

 point in the prolongation of y y, and at the other, after being- 

 led through the hollow axis xx, is connected at a, /3, 7, 8 to 

 the windings in a x and a. 



If now the axis y y is made to rotate, then the axis x x must, 

 on account of its being geared through b b u make one revo- 

 lution for each revolution of y y, so as to leave the flexible 

 cable untwisted. Hence if the yy axis be placed vertically 

 or horizontally in the magnetic equatorial plane of the earth's 

 field, its rotation will induce currents in the a and a, 

 windings; the simultaneous rotation about xx does not in 

 any way affect the results. 



As will be seen, the uncertain sliding-contacts are by this 

 means entirely eliminated. 



Degerloch ( Wttbg.), June 27, 1902. 



LYI. The Jacobian of the Primary Minors of an Axisymmetrie 

 Determinant ivith reference to the corresponding elements 

 of the latter. By Thomas Muie, C.M.G., F.R.S* 

 ('i)TT would appear that in certain recent work of Professor 

 X Karl Pearson's he had occasion to make use of a 

 determinant | r\ n | in which r% == rji and r u = 1, and from 

 which was formed another determinant | p hl | such that in 

 every case pij =Rt>7 VK« fyj 9 the special problem which pre- 

 sented itself being the evaluation of the Jacobian 



d(plg» Pl3i • » ■» Pn—hnj- 



(K?'l2) r \i, • • •> **-l,n) 



Mr, Arthur Berry, to whom the problem was transferred, suc- 

 cessfully solved it, and communicated the result to the 

 Cambridge Phil. Soc. in October 1898 |- His process con- 

 sisted in showing that the Jacobian required was obtainable 

 from two other Jacobians of lower order 



d(P l2 < Pl3* • • •* Pn-2,n-l) d'^ln; r 2 „, .... ^n-!,*. ) 



CH/12> ''135 • • •? ?V-2,n-l) B(^ln, p2n, • • ., pn-1, n) 



'■■■ Communicated by the Author. 



t Pearson and Eilon, " On the Probable Errors of Frequency Con- 

 stants," Phil. Trans. A. cxci. pp. 229-311 (1898); Berry A., "On the 

 Evaluation of a certain Determinant," Proceedings Cambridge Phil. 

 Soc. x. pp. 2-10; Crawford L., "On the Evaluation of a certain 

 Determinant/' Proceedings Edinburgh Math. Soc. xviii. pp. 25-27. 



2L2 



