Arithmetical Relations between Chemical Equivalents. 387 



I the moon's distance are more consistent and satisfactory 



ise depe"-^- — — *^- "' ---^ j.-i:^--.- i 



The lunar effect ii 

 part in perigee and 1 

 is in apogee. 



The Prague results are the same, viz: a greater horizontal 

 force at and after the moon's apogee than at and after her perigee ; 

 a three years series of observations at Milan, however, do not 

 agree therewith. In no branch of magnetic research would ad- 

 ditional results from independent observations, particularly at 

 stations widely apart, be more acceptable and valuable than in 

 the study of the lunar effect in its various manifestations. 



In previous numbers of this Journal I have published a series 

 of papers on this subject, one point of which has been subjected to 

 criticism ; namely, that I have introduced, in order to complete 

 certain series, negative equivalents, as is alleged, without giving 

 any explanation of such a conception. 



In answer, I mav observe, that I have not used the expression 

 attributed to me. " I have never once in the whole series of 

 papers referred to, spoken of negative equivalents. Such an 

 expression would I conceive, be an absurdity. Any negative 

 quantity taken in an isolated sense is, as Carnot has proved, an 

 absurdity. But I have pointed out that by carryiDg certain 

 decreasing arithmetical series to successive terms, the equivalents 

 of well marked series of chemical bodies were obtained, and 

 that finally when we reached a point at which the last term was 

 less than the common difference, the series might yet be contin- 

 ued, and the equivalents of other elements, admitted by all 

 chemists to belong to the same natural group, might be obtamed, 

 although with negative signs affixed. For example, if commen- 

 cing with antimony, we subtract a number correspondmg nearly 

 ^vith 45 we obtain in succession the equivalents of arsenic and 

 Pliosphorus. With phosphorus we reach a term, the numerical 

 value of which is less than the common difference. We cannot 

 therefore carry the series forward another term without encoun- 

 tering negative numbers. Kevertheless there remains another 

 Diember of the group, nitrogen, intimately bound to it. Is it 

 ^ot then a matter of great interest to observe that this last mem- 

 ber of the group, apparently cut off from it, is reached, although 

 ^vith a negative sign, by simply carrying the series another 

 step ? 

 Am. .Jol-r. Sci.-Secosd Sekies, You XXXIV, 5o. m.-^ov., 1862. 



