OF WASHINGTON. 205 



the enormous number of 5,904,900,000 individuals during the month or 

 six weeks of her existence. Probably the daily birth, as given by Latreille, 

 is above the truth, yet I have witnessed the birth of eight young from the 

 same mother in six hours, viz., from ten o'clock in the morning to four 

 o'clock in the afternoon. However this may be, neither Tougard nor 

 Morren is satisfied with Latreille's billions; both state that quintillions 

 are within the capabilities of a single mother's efforts. Prof. Huxley 

 makes a curious calculation, though for a different purpose, which at any 

 rate affords some approximate idea of what a quintillion of Aphides might 

 mean. Assuming that an Aphis weighs as little as y^Vu of a grain, and 

 that it requires a man to be very stout to weigh more than two million 

 grains, he shows that the tenth brood of Aphides alone, without adding 

 the products of all the generations which precede the tenth, if all the 

 members survive the perils to which they are exposed, contains more pon 

 derable substance than five hundred millions of stout men; that is, more 

 than the whole population of China! " 



In a foot note he then goes on to show 



" that Prof. Huxley's graphic illustration, nevertheless, much underesti 

 mates the real quantity of animal matter capable of elaboration fi-om one 

 single rose Aphis in a year. 



" Basing the calculation, for simplicity, upon the supposition that every 

 Aphis lives twenty days, and that at the expiration of that period each 

 Aphis shall have produced twenty young and no more, then, at the expira 

 tion of three hundred days only, the living individuals would be 32,768,- 

 000,000,000,000,000, or equal to the weight of 1,638,400,000 men." 



* # * "A. mathematical friend remarks that this calculation does 

 not express the real rate of increase, since it supposes the progeny of 

 the first Aphis to be produced at once, and not to commence producing 

 until the expiration of the first twenty days. To this same friend I am 

 indebted for the annexed calculation. 



" If we suppose the progeny of the first Aphis to equal 20 in twenty days, 

 and this progeny to begin producing, when five days old, 20 young, each 

 of which on attaining the age of five days begins the propagation of 20 

 young, and completes, also, that number in twenty days; 

 " Then, at the end of twenty days from the commencement of first 



Aphis production there would be direct issue = 20 A 



" At the end of fifth day, progeny A begin to produce, which at 



the end of first twenty days will altogether equal 15 -|- 14 -j- 13, 



-j-12, &C., -(- 2 + 1 = 120 B 



" At the end of tenth day, 'progeny B begin to produce, which at 

 the end of the first twenty days will altogether equal 10 -j- 9 

 + 8, &c., +2 + i = 55 C 



" At the end of fifteenth day, progeny C begin to produce, which 

 at the end of the first twenty days will altogether equal 5 -j~4 

 + 3 + 2 + i = i5P 



" Total at the end of 20 days equals A -|- B -j-C-j-D = 210 



