Cambridge Philosophical Society. 69 



the errors show a certain degree of systematic character over ex- 

 tensive districts, so as to alter the declination or inclination a degree. 

 The inclination appears to me to be very incorrect in the meridian 

 of Alexandria. In India the few results of Elliot's given in the 

 Philosophical Magazine from the Proceedings of the Royal Society, 

 accord extremely well with my calculations. I subjoin a few points 

 of comparison : — 



North Pole in 70° 7' N., 263° 37' E. Ross's observations give 

 70° 5' N., 263° 14' E. For the South Pole, 74° 6' S., 152° 47' E. 

 seems to agree less closely with Ross's map, although the inclina- 

 tions observed in the neighbourhood agree well with the calculated 

 ones. 



Maximum of total force in the northern hemisphere 1871*8 in 54 21 N. 265 53 E. 

 (Error compared with Lefroy's observations +6*4 in 54 1 N. 260 1 E. 



+0-8 in 55 6N. 267 4E.; 



+4-6 in 50 2 N. 264 E.) 



For the force in the southern hemisphere, 2027" 6 in 64° 36' S., 

 144° 34' E. is perhaps less correct, but there are in the S. hemisphere 

 some striking anomalies in the observations. 



The probable error of the force is 19*1 ; if however some groups 

 which are at any rate not very correct are omitted, it becomes a little 

 less than 15. For the inclination, 31'* 1 ; for the declination, 41'* 3. 



CAMBRIDGE PHILOSOPHICAL SOCIETY. 

 [Continued from vol. v. p. 464.] 



April 25, 1853. — Professor Challis gave a lecture on the Adjust- 

 ments of a Transit Instrument. 



A paper was read by Professor De Morgan on the Principle of 

 Mean Values, and an addition to a paper on the Symbols of Logic, 

 &c. in vol. ix. part 1 of the Society's Transactions. 



Though the heading of this paper describes one of its main results, 

 yet it might with equal propriety have been styled a discussion of 

 some points of algebra, with reference to the distinction of form and 

 matter. This distinction, it is contended, is more extensively applied 

 in algebra than in logic, though more recognized in logic than in 

 algebra. Looking at the disputed points which exist in the higher 

 parts of mathematics, and feeling satisfied that they will never be 

 settled until the separation of form and matter is both visible and 

 complete, the author makes a first attempt towards the examination 

 of the question how far this yet remains to be done. A number of 

 comparisons are made between algebraical and logical process, in 

 the course of the inquiry, illustrative of the opinion entertained by 

 Mr. De Morgan, that logic, as treated, requires the interposition of 

 the algebraist, and cannot, except by aid of algebraical habits, be 

 rendered a complete exposition of the forms of thought. In digress- 

 ive notes, he combats the opinion that a generalization of the quan- 

 tity is, as asserted, a new material introduction. He argues against the 

 too mathematical tendency of some of the logicians who have endea- 

 voured to extend the ancient system, especially the attempt of some to 

 make the logical import of the proposition nothing but a comparison 

 of more and less, and an equation or non-equation of quantities. He 



