The Melopliagus, or Sheep-TicJc. 439 



PLATEAU'S AEITHMETICAL PROBLEM— A NEW 



METHOD. 



BY JAMES J. HOOTON. 



I have just read in this month's number of the Intellectual 

 Observer a translation of a paper communicated by M. Plateau 

 to the Belgian Academy, in which that gentleman supplies a 

 general rule for the solution of a certain problem involving the 

 properties of numbers. It occurs to me that a more direct 

 method of dealing with this simple matter would be to assume 



N = ^-^- L where N is the required multiplicand, n the 



given multiplier, and 11111 , a number containing the 



smallest iterating figure, of which any other similar number 

 would, of course, be a multiple. Adopting this equation, it 

 will be found by experiment that for even values or multiples 

 of 5 given to n, the quotient of 1111 . . . . -f n or N will be a 

 number with a figure or figures recurring, ad infinitum, and 

 that, consequently, the problem fails for all such values of the 

 independent variable (n). For all other values of n, the quo- 

 tient is terminable, and we arrive at one result without the aid 

 of " periodic decimal fractions," etc. 



THE MELOPHAGUS, OR SHEEP-TICK. 



BY L. LANE CLARKE. 

 {With a Tinted, Plate) 



When the farmer, careful for the well-being of his flock, gives 

 the order for a sheep -washing, or ' ' a ticking " — and thousands 

 perish of the parasites which irritate the sheep — doubtless the 

 farmer is right; we have dominion over "the creeping thing/' 

 and reason to judge of its proper rate of increase. Neverthe- 

 less, that same sheep-tick presents an interesting and thoughtful 

 object for a naturalist, who, entering into the mysteries of 

 organic life, gathers up every minute variation and modification, 

 holding each as a clue to guide him through the labyrinth of 

 Almighty wisdom, which the mere classification of genera and 

 species fails to grasp. 



Comprised within the order Diptera, or two-winged flies, 

 we find several genera which have no wings at all : the 

 apterous and suctorial Pulex, and the apterous and pupiparous 

 Eproboscidae ; though amongst these latter we have the winged 

 Hippobosca, or horse-fly, the Ornithomyia, or bird-fly, and the 

 Stenopteryx, or swallow-fly. 



