131

The diam. of a sphere of water which shall weigh .00000324 milligrammes is given by

   πd3 / 6 =    .00000324

   d = (calculations) log .01836

15/18 = 5/6    (illeg)

Diamr. of sphere of water weighg. .00000324 Millgrs is (illeg) .01836 millimètres

Or Diamr. of sphere of water weighg 1/20,000,000th of a grain is .0007225 of an inch

 .0005 [÷] .0152 [=] .0329

.015 [÷] .0005 [=] 30

.015 [÷] .0002 [=] 75

131v

The same thing worked inversely

To find the weight of a sphere of spec. gr: 1.758 & of diam: .0152 of a millimètre

(calculations)

Weight = .000003239 millgrammes

 To find the wt. of a sphere of sp. gr. 1.758 of diam .0005986 of an inch—

The volume is π/6(.0005986)3 in cubic inches & the wt. of a cub: in: of this sp gr:

(calculations)

= 1/20,000,000th of gr:

132

1 grain = 64.79896 milligrammes

1/20,000,000th of a grain = [calculations] = 1/300,000th of a milligramme ‹very› nearly

a kilgramme is the wt. of a litre of water

a kilogramme = (1000)2 milligrammes

a litre = a cubic decimètre = (1/10 x 1000)3 millimètre

[calculations]

1 cubic millimètre

= 1 milligrammes

Let d be diam: of a sphere in millimètres

Then a sphere of diam. d of water weighs πd3/6 milligrammes & a sphere of this diam. of sp: gr: ρ — πρd3/6

To find the diam. of a sph: of sp: gr: 1.758 which weighs .000003239948 millgrs.

[calculations]

d = .01521 millimètres

∴ The diam. of a sph: of sp: gr: 1.758 & weighing .00000324 milligrs. is .0152 millimètres = 1/66 millimètre or The diam: of a sph: of sp: gr: 1.758 & weighing 1/20,000,000th of a grain is .0005986 of a inch = 1/1667th of an inch

The smallest object visible in the microscope is betw: .0002—.0005 millimètre that is between 1/5000th and 1/2000th of a millimètre, that is between 1/30th & 1/75th of the diam. of our sphere

133

a cubic foot of water weighs 1000 oz = 1000/16 x 7000 grains = 700 x 252 gr

[calculations]

1 cub. in of water weighs 28 x (25/12)3 grains ∴ weight of sphere of d inch. diam of water = πd3/6 x 28 x (25/12)3

Suppose it weighs 1/20,000,000 gr

[calculations]

Diamr. of sphere = .0007225 of an inch [=] 7/10,000th of an inch.

[calculations]

Diam. of sphere of water weigh 1 grain = .1961 of an inch = 1/5th of an inch nearly

[calculations]

The diam. of a sphere of specific gravity = 1.758 and weighing 1/20,000,000 of a grain is .0152 of a millimètre  or .0005986 of an inch